A model of strategic preemption: Why do Post-communists hurt themselves?

: Why do political actors pass legislation that seemingly hurts them? Lustration laws limit access to public of ﬁ ce of the ancien regime's collaborators and hurt members of post-communist parties in East-Central Europe. So why has lustration in Poland, Hungary, and Bulgaria been passed when post-communist parties held parliamentary majorities? Why did the post-communist party in Romania switch from no-lustration to pro-lustration after the 1992 elections? We explain this phenomenon by electoral timing and rules of procedure in legislatures. Speci ﬁ cally, we develop an agenda-setter model with a ﬁ nite number of parties, imperfect information, and multiple potential medians. Our main argument can be summarized as follows: Suppose that the Post-communists do not introduce any lustration bill and then lose proposal power in elections. If Anti-communists come to power, they are sure to introduce a harsher bill, and the median of the legislature may prefer such a bill to a no-bill status quo. Post-communists can prevent such a scenario by implementing a mild bill themselves. If they manage to appease the new parliamentary median, they will block a harsher bill that would be implemented after they lose power. Additional results show how electoral perspectives and uncertainty affect and modify this typical scenario. We test our model with an exhaustive analysis of all cases from East- Central Europe that meet our assumptions that a Post-communist party is in power and no lustration bill is already in force.


Lustration as a strategic weapon
Why do legislators and executives sponsor bills that are different from their ideal policy? Examples of such "self-hurting actions" include agrarian parties sponsoring bills that limit state subsidies for agriculture or social democratic parties sponsoring tax cuts. A prominent example of such behavior in East-Central Europe is legislation banning from public office members and collaborators of the ancien régime sponsored by post-communists, known also as successor communist parties (Pop-Echeles 1999).
In 1990, the Bulgarian parliament dominated by Post-communists appointed a special commission to produce a list of persons who had collaborated with the secret police during the communist era 4 . The final list included the names of eighty deputies, that is, one-fifth of all legislators. In December 1993, the Post-communists holding majorities in both houses of the Romanian legislature adopted similar legislation. The law mandated the publication of the names of former agents and informers of Securitate, the Romanian secret police in . Proven informers were forbidden from holding public office (Schwartz 1995). In Hungary, the 1996 lustration act revealed the links of MPs with the secret police and named members of the communist pre-transition government who had been receiving reports from the secret police. This act was passed by a parliament with a post-communist absolute majority. The same legislature issued a declassification bill that in September 1997 opened to the public the secret files of the former regime. Finally, in 1997, the Polish Lower House dominated by Post-communists adopted a bill that instituted the screening of candidates for MPs, justices, and attorneys for their connections to the communist secret services between 1944 and 1990. In addition, the Polish postcommunist president initiated a declassification law and proposed a bill founding the Citizens' Archive. Its goal would be to collect, organize, and distribute copies of the ancien régime's documentation to the public (Kwasniewski 1997).
In all these cases, the post-communist successors of the old regime passed laws that seemingly inflicted immediate and substantial political harm on themselves. These laws eliminated many of their members and supporters from public office outright but, more importantly, prevented some of their candidates from running in the upcoming electoral struggles. 4 The former communist parties that have adapted themselves to competition in democratic elections, sometimes labeled as "communist successor parties," are here referred to as "Post-communists." We call "Anti-communists" the parties that insist on harsh treatment of members of the communist ancien régime. The hyphenated versions of both nouns are used due to their relatively highest frequency among Google Scholar hits. For all parties mentioned in this article, their original acronyms, original and English names, spatial positions, and other data are listed in Appendix 3. Bills similar to the ones described above constitute "lustration laws," that is, legal measures that are adopted in countries following transitions to democracy to verify whether persons running for legislative office had collaborated with the ancien régime (Nalepa 2010). Proven collaborators are either explicitly banned from running for office or their past is revealed to the public, which is likely to end their political careers. In general, lustration, decommunization (banning from public office former communist party members or leaders) and declassification (revealing to the public the contents of secret police files of the authoritarian era) are most important laws constituting transitional justice legislation (TJ) that deals with various wrongdoings of the past regime in the aftermath of regime change.
Neither the TJ literature, nor the literatures in post-communist politics have examined post-communist "self-lustrations." Our goal is to explain why Postcommunists "punish themselves." It is useful to pro vide some intuition for the explanation we offer. First, in four out of eight countries where lustration laws were adopted for the first time in the 1990s and Post-communists were in power at the time of adoption, they expected to lose the upcoming elections. Second, the laws were passed either in the close proximity of elections or during cabinet crises that increased the probability of early elections. (In Lithuania, "de-sovietization" laws with some characteristics of lustration were adopted early by a Soviet-elected parliament. In the remaining three countries that adopted lustration, Post-communists never held a parliamentary majority.) In other words, lustration is often introduced either when post-communist parties are relatively weak, or when they are very strong but are about to lose power. Our explanation of the Post-communists' apparently puzzling behavior builds on these observations. We argue that Post-communists act under constraints of legislative institutions. They adopt seem ingly self-hurting bills when they expect to lose the upcoming elections to anti-communist opponents who want to punish them more harshly. To prevent this harsh legislation, they preemptively pass milder bills that appease the median legislator and make him reluctant to accept anti-communist pro posals. We formalize our argument with a game-theoretic model of agenda setting. In their seminal contribution, Romer and Rosenthal (1978) introduced an agenda-setter model that explains how the final outcome of the legislative process results from an interaction between a proposer and the median in the legislature. Our more complex version of their model formalizes the following core intuition: Suppose the Postcommunists anticipate losing proposal power to anti-communist forces. If they do not adopt any bill, then they risk suffering from very harsh lustration, because the legislative median may prefer harsh lustration to no bill at all. Post-communists may prevent this scenario by imple menting a mild bill themselves. If their bill appeases the new parliamentary median, it prevails when they lose power. In the original The scenario described above implicitly assumes adopting bills under closed (or restrictive) rules of parliamentary decision-making (Denzau and Mackay 1983, Gilligan and Krehbiel 1987, Weingast 1989, Baron andFerejohn 1989, Baron 2000), where the proposed bill cannot be modified on the floor of the legislature. The median has to "take it or leave it." In contrast, under open rule procedures, the role of the proposer of bills is insignificant since all his proposals can be more or less freely amended on the floor. The bill favored by the median voter in parliament is ultimately the proposal that gets passed 6 . The rules of procedure were closed in all but one case we consider here 7 .
Our argument fits well into the broader literature on legislative institutions. The analysis of legis lators passing legislation distant from their ideal outcome in expectation of a turnover in power can be applied to various types of bills. We expect "self-hurting actions" to occur whenever (1) the proposal power is likely to shift from incumbents to challengers and (2) there is a veto player between their ideal points. When these two conditions are met, agrarian parties may sponsor a bill that limits state subsidies for agriculture or social democratic parties may sponsor tax cuts. Our model of strategic preemption accounts for such counter-intuitive behavior of political actors within the framework of formal theory.
The paper is organized as follows: The next section provides a brief review of the relevant literature on transitional justice. Then, we formalize the argument and define conditions under which it is ratio nal for Post-communists to "hurt themselves." The following section derives our predictive hypotheses from the main model, describes our data points and states measurement issues. Next we analyze the cases of legislative action or inaction in Bulgaria, Hungary, Poland, and in two Romanian legislatures. These five cases exhaust all instances in which Post-communists were in power and no prior lustration law had been introduced. Appendix 1 includes the figure illustrating the timeline of transitional justice legislation. Complex mathematical details and 5 Banks (1990) extended the Romer and Rosenthal model to asymmetric information among voters, represented as "noise" around the reversion level. Lupia (1992) applied this model to California state referenda. To our knowledge, uncertainty about the location of the median on part of the proposer has not yet been examined. DECYZJE NR 21/2014DOI: 10.7206/DEC.1733 proofs are relegated to Appendix 2. Appendix 3 lists main political parties that were involved in TJ in Bulgaria, Hungary, Poland and Romania.

Transitional justice: a brief introduction
Collaboration scandals continue to influence East-Central European local politics. Files of the commu nist secret police have ended political careers and toppled cabinets. In 2002, in Hungary, a Budapest daily revealed that the new Prime Minister, Peter Medgyessy, had been an undercover agent of the military counterintelligence. He kept his post only after agreeing to appoint an ad hoc parliamentary committee to screen all cabinet ministers between 1990 and 2002 for collaboration with the Hungar ian secret police. In the same year, General Bruce Jackson made screening the military an ultimatum condition of Bulgaria's membership in the NATO. Similar demands have been made in the context of Romania's candidacy for the EU. The list of collaborators of the Communist Secret Police published in Slovakia in March 2005 included the Speaker of Parliament, Pavol Hrusovsky, the Secretary of State, Jan Hurny, and other key politicians. Two of them had to resign their positions immediately. In June 2006, the Marcinkiewicz cabinet of Poland fell after the deputy Prime Minister Zyta Gilowska resigned in the midst of allegations of spying on her friends from underground Solidarity. These ex amples illustrate that politicians' conduct prior to the transition is still under scrutiny in East-Central Europe. At the same time, voters care less about their politicians' past than the politicians themselves. But since voters cannot punish elites for giving undue weight to the dimensions they consider rela tively unimportant, such dimensions are particularly vulnerable to strategic exploitation. Elites can manipulate relevant laws to their advantage while avoiding electoral accountability.
Politicians in East-Central Europe feel very strongly about lustration because such legislation is directly tied to their interests. A harsh bill may end, and often has ended, careers of former collab orators. Parties who have fewer ex-collaborators amongst their ranks may benefit from introducing lustration laws to eliminate electoral competition. If politicians seek reelection and parties desire to maximize their legislatative representation, they must include lustration in their political calculus. It is hardly surprising that introducing, changing, or vetoing transitional justice is a popular activity as illustrated in Fig. 2 Poganyi 1997). Its normative component, rooted in legal and constitutional theory, examines possible justifications for retroactivity and problems created by retroactivity (Sa'adah 1998). Main questions include: "To what extent should the ideals of rule of law be bent for the sake of punishing the wrongdoers?" and "Can acts that were legal according to authoritarian constitutions be prosecuted?" (Nino 1996, Welsh 1996 Another strain of TJ research asks positive questions. One may inquire why new democracies attempt to rectify the ancien régime's wrongs (Schmitter and O'Donnell 1986); who are the actors re sponsible for implementing TJ (Elster 2004); and whether TJ has led to reconciliation (Gibson 2004). Related literature deals with negotiated transitions and predicts that autocrats concede to democrati zation only after they are guaranteed that the new democratic institutions will not prosecute members of the ancien régime (Schmitter and O'Donnell 1986, Przeworski 1991, Colomer 1991, Omar 1996, Nalepa 2010. Examples of such institutional guarantees include constitutions that render retroactive legislation illegal and electoral laws that give the outgoing regime an upper hand.
Finally, there is a considerable body of literature in comparative politics devoted to explaining the surprising come-back of post-communist parties in East-Central Europe (Ishiyama 1999, Grzymala-Busse 2002, Bozoki 2002. It is indeed surprising that successors of parties responsible for decades of authoritarian rule, who were so unpopular in 1989, would be winning elections only a few years later. But even more puzzling than their revivals, is that Post-communists adopt policies that seemingly hurt them.

The Model
We begin with an intuitive game illustrating the main mechanism at work. Next, we consider a more complex model that relaxes the assumptions of perfect information and three parties.
Both models have a TJ issue space [0,1], shared by all players. A point in [0,1] represents the relative harshness of TJ legislation. 0 is interpreted as a situation of no TJ while 1 is the relatively harshest TJ. Harsher laws screen more positions and/or apply tougher sanctions to positively screened lustrants. For instance, the Hungarian 1996 bill covered only 600 candidates running for highest public office and would be located close to 0. The Czech 1991 lustration act required that over 420,000 persons obtain lustration certificates from the Ministry of Interior. It would be located near 1. Players in all games have Euclidean preferences: if a player has an ideal point w Î [0,1], then his payoff from an outcome v Î [0,1] is the negative distance from v to w, i.e., -|v -w|.

Example: Three parties and known median
Our illustrative example is a simple sequential game. There are three players: PC (post-communist party), M (legislative median), and A (Anti-communists), with their bliss points 0, m, and 1, respec tively. We assume for simplicity that the median is leftleaning, i.e., that 0 < m < 1/2. The sequence of play represents the key aspects of the political process: Period 1: PC unilaterally introduces a status quo y;

Period 2: A proposes alternative legislation x;
Period 3: If x = y, x becomes law; if x ¹ y, M decides between x and y.
Since our first game involves perfect information, we can find subgame perfect equilibria (SPE) with the help of backwards induction. We are interested both in equilibria and in the properties of PC's SPE strategies that would shed light on the rationale behind PC's behavior. The intuition behind the solution unfolds as follows (we skip minor mathematical details that receive their due treatment in Appendix 2): In the last period, M chooses the proposal that is closer to m, its bliss point. Party A assumes that M plays its SPE strategy. If y £ m, it proposes the greatest x on the opposite side of m that is still not worse for M than y, that is, x = 2m -y. If y > m, this is the best A can get, since M will not accept anything harsher. Thus, the best outcome that A can get against PC's y is 2m -y for y £ m and y for y > m. Finally, consider PC's best option assuming A and M's SPE strategies. Any strategy y > m or y < m fares worse than y = m, since it leads to an outcome y or 2m -y, respectively, which is greater than m. PC's best choice in SPE is to propose m.
The game explains how the incumbent PC may have incentives to replace its ideal policy, 0, with mild TJ legislation. While PC has a unique SPE strategy m, A has many. For instance, if PC chooses m, A can offer any x, since M will choose m regardless of x. The existence of multiple equilibria is inconsequential, since, as our first result makes clear, only one outcome can happen in equilibrium.

The model of preemptive legislation
In our example, PC knows with certainty the future position of the legislative median and there are only three parties. We relax these assumptions in the main model, which is defined as a parametrized family of sequential games. For specific values of the parameters, which include the number of parties, their ideal points, and the probability distribution for the position of the future median, the model becomes a specific game.
There are n > 2 parties, including two principal players PC and A, that compete in the elections. The parties are denoted as PC = M 1 , M 2 , ..., M n = A, and their ideal points as 0 = m 1 £ m 2 £ … £ m n £ 1, respectively, where m n > 0. Moreover, PC is risk-neutral. The probability of winning the median position by party M i is equal to p i . The case of multiple medians is excluded. The distribution may be interpreted as "objective" or as PC's ex ante beliefs about the location of post-election median. In line with our empirical cases, we assume that if neither PC nor A win a majority in the elections, the proposal power always goes to A. Every specific game is played according to the following scenario: If 1 < i < n, A makes a proposal x against y. This is the case when a moderate party becomes the median and the proposal power in the new legislature goes to A. If x = y, the outcome is x and the game ends. Otherwise, the game continues.

Period 4 (median party's choice): M i selects between x and y.
The game has four periods except in special cases; for instance, when PC and A propose the same legislation, it automatically becomes law. The protocol is also shorter when PC or A are chosen as medians and have full control over legislature. Note that our example from the previous section is a special case of the model, with one left-leaning party, M 2 , and p 2 = 1.
The model could be made even more general. For instance, one could relax the assumptions that power is initially in the hands of PC, that A becomes the proposer after PC fails to win an absolute majority in the elections, etc. However, the cost of such modifications is, obviously, increased complexity. The benefits for our project are null since in all our empirical cases the present model's assumptions are satisfied. In certain empirical cases, a strong president requiring a super-majority to override his veto or a president supported by the Constitutional Court can play the role of an institutional median. More generally, the model is applicable to various cases when proposal-making power is changing hands and a veto-player's ideal point is located somewhere between the ideal positions of successive proposal makers. While including a veto player is a useful option due to the importance of veto players in politics (Tsebelis 2002), we believe the present formulation to be more intuitive.
Proposition 2 examines the most fundamental properties of SPE. Let's define Y* Ì [0,1] as the set of all SPE strategies for PC, that is, strategies that are best replies to other players' strategies in all subgames.

Proposition 2 (i) Every game has at least one SPE;
(ii) For every game, Y* Ç { m 1 ,…, m n -1 } ¹ . If p n < 1, then for y such that m i < y < m i + 1 for some i, y Î Y* iff m i , m i + 1 Î Y* and for no j, 2m j -1 Î (m i , m i + 1 ). In such a case, [m i , m i + 1 ] Ì Y*; (iii) Within all n-player games, games with multiple SPEs generically do not exist.
Comment to Proposition 2: In (i), the existence of SPE is established.
In (ii), we characterize the equilibria and the SPE strategies for PC. In every game, PC has at least one SPE strategy among the bliss points of parties M 1 -M n -1 . In other words, PC, when looking for optimal policy y, may consider only the ideal points of all parties less radical than A. In addition to single points, an entire interval may consist exclusively of PC's SPE strategies. However, this happens if and only if the bliss points of neighboring parties are SPE strategies and if no point in its interior is equal to 2m j -1.
Finally, (iii) says that games "almost always" have a unique SPE. Multiple equilibria are extremely unlikely. Thus, we may safely assume that in real world parties in the situation of PC may disregard the troubles with multiple equilibria and multiple optimal strategies. They choose between the ideal points of potential medians and look for a single optimal strategy.

Empirical hypotheses
We apply our model to the last months before the elections, when the decision whether to introduce TJ or not has to be made. Under some circumstances -such as an unstable cabinet coalition that makes early elections likely -PC may consider such a decision earlier. We will not formalize the timing aspect of the decision process although such a formalization could be implemented. The multiplicity of parameters in the model implies that by fixing them we can prove a variety of specific theorems in the form "in CASE X, EVENT Y takes place," where both X and Y may vary. When we apply these theorems, or "empirical hypotheses," to empirical cases, they generate very specific testable predictions about player decisions. We consider four empirical hypotheses of such sort. We state the empirical hypotheses H1-H4 and their proofs formally as Proposition 4 (h1)-(h4) in Appendix 2.
The values of our independent variable CASE that are specified in our empirical hypotheses fix certain parameters of the pre-electoral and post-election empirical situation. Our dependent variable EVENT describes our predictions. When CASE refers to a pre-electoral situation, EVENT denotes the action taken by the Postcommunists and may assume values "PC introduce TJ" versus "PC does nothing." When CASE refers to a post-electoral situation, EVENT accounts for the final outcome of the game. Such an outcome may be the victory of the post-communist proposal that results in "no post-electoral TJ." The alternative outcome for EVENT is the victory of an amended proposal and new "harsher post-electoral TJ." Our first two empirical hypotheses, H1 and H2, examine the PC's incentives for introducing TJ. Clearly, refraining from action may be their best strategy under certain circumstances. We specify a sufficient condition for such an outcome in H1. If PC expects with probability greater than 1/2 to be the future median, that is to maintain legislative majority after the elections, it is too strong to worry about undertaking preemption.

H1 (Post-communists are the likely median):
If the Post-communists expect with probability greater than that they will win a majority of seats, they do nothing.
Our second hypothesis examines what happens when the Post-communists are unlikely to win the median position.
H2 (Post-communists are unlikely to be the median): If the Post-communists estimate the probabil ity that the post-election median will be among the other left of center parties to be greater than they will win a majority themselves, they introduce TJ.
When PC has smaller proability to become a median than the probability of all other center-leftist parties combined, then it has an incentive to propose a TJ bill. Under proportional representation, even a party enjoying a 30-35% support in public opinion polls (which is high by East-Central European standards), has little chance of winning a legislative majority. But this is precisely what is required of an end-ofspectrum party, such as PC, to be the median. A moderate party has considerably better odds. All it requires is that it command legislative majorities both with all parties to its left and to its right. The more specific Proposition 4 (h2) in Appendix 2 asserts that the TJ bill will be located at m 2 or even farther to the right. The conditions in H1 and H2 are not exhaustive. However, we need not worry about other possi bilities, such as when PC expects to lose the median and PC is the only left of center party because the conditions from H1 or from H2 cover our entire universe of empirical cases.
The next two hypotheses examine what happens after the elections under two different electoral scenarios. Recall that unless PC wins the elections, the proposal power goes to the Anti-communists but after PC makes its choice, the actual median is chosen in the elections. H3 describes a choice of PC that is too optimistic and the actual median is farther to the right than their proposal, y. H4 describes a choice that is correct or too pessimistic because the actual median is y or less than y.

H3 (Overly optimistic estimates): When the median's position is m i > y, there is a new post-electoral TJ that is harsher than y.
In H3, the Anti-communists have an incentive to exploit the resulting opportunity as predicted by a standard agenda-setter model: they go as far to the right as possible. Proposition 4 (h3) in Appendix 2 again offers a more specific prediction for the final bill to be equal to min {2m i -y, 1}.

H4 (Overly pessimistic estimates): When the median's position is m i £ y, there is no post-electoral TJ.
When PC are too pessimistic and overestimate the median, or when they are correct in their esti mates, there is no TJ activity in the aftermath of elections. A cannot effect change: the median already has its most preferred outcome or the only acceptable change is to the left of the PC's proposal.

Methodology
To demonstrate that politicians act strategically about lustration, we use 101 semistructured inter views with some of the most important politicians in Poland, Hungary, and the Czech Republic. Our respondents include the former President of Hungary Laszlo Solyom, the former Czech prime min ister Petr Pithart, the former Polish premier Jan Olszewski as well as numerous ministers and MP's. As an illustration of the evidence presented by these data, consider the following comment from a postcommunist MP, Jerzy Dziewulski, reporting how the Polish president Kwasniewski justified the need for a preemptive strike: "Jurek, listen: we just don't know when [the hard-line Anti-communists] will start revealing the past [about our collaboration with the communist secret police.] What we do know is that they'll do it in a nasty way." that SLD "knew well that it was better to come forth with a soft bill than wait for the swing of the [electoral] pendulum and suffer from a harsh bill" (Interviews 2004: MK). State ments from other politicians are equally illuminating. They support the claim that the Post-communists acted strategically and that they believed that all other players act strategically.
Although we use data from elite interviews to illustrate various points, our empirical tests go be yond anecdotal evidence.

Data
We collected data on electoral results and party positions on TJ. We also reconstructed PC's beliefs about the future median. The data are presented as case studies analyzing the passage of lustration laws. It is important to emphasize that we analyzed all cases relevant to our main question.
Out of all post-electoral terms in all post-communist countries, we selected those that satisfy the following criteria: C1. The country was democratizing or democratic in 1990s; C2. PC was at least the senior party of a ruling coalition; C3. The status quo was null, i.e., no TJ introduced earlier was in force.
Various countries failed to satisfy two or more criteria. The reasons for excluding autocratic regimes are obvious: If actual decision-making is located outside of the parliament and other de mocratic bodies, whatever happens in the legislature may not be relevant to the outcomes. In such a case, our model is not applicable. No non-European post-communist country satisfies C1. Thus, Georgia is excluded because it democratized too late (in 2003), while Russia cannot be regarded as an undisputable democracy. For Europe, our criterion coincides with becoming a European Union member, as such membership followed long and careful scrutiny of a country's political system. Thus, Albania, Ukraine, Moldova, Belarus, and post-Yugoslav countries (except for Slovenia) are excluded as well.
Criteria C2 and C3 further narrowed down our universe to ten cases. We considered only those countries where at some point the proposal power was in the hands of PC and that no TJ was im plemented earlier. These assumptions are built into our model and simply represent the conditions that motivated our puzzling question: Why would Post-communists voluntarily hurt themselves? In Slovenia, the Post-communists were never sufficiently powerful after the breakdown of Yugoslavia. In Czechoslovakia, a harsh lustration law was quickly introduced by the first post-1989 government even before the Velvet Divorce. The Czech Republic and Slovakia inherited it and, therefore, their status quo was never zero.
The three Baltic republics turned out to be especially challenging. The Balts inherited an issue specific only to countries that were parts of the Soviet Union. Some of the former communists claimed to be "radishes," that is, "red only on the outside". Many radishes "joined the nomenklatura for ca reer purposes, some did so for patriotic reasons-filling a position in order to deny it to a Russian colonist" (Taagepera 2005, personal communication). The desovietization laws intended to separate such radishes, who would not go as far as to provide intelligence to the Russian KGB, from the "red beets," that is, the former KGB agents. The issue of "de-sovietization" dominated TJ in the Baltic states and the resulting legislation partially overlapped with lustration. This peculiarity made our criterion C3 ambiguous with respect to the Baltics.
Since Estonia and Latvia never had Post-communists in power, they are excluded on the basis of C2. The case of Lithuania is less clear. Supported by the radishes, two quasi-lustrative "desovietiza tion" laws, Decree No 418 and Law No I-2115, were passed before the 1992 elections, which were won by two post-communist parties (Kritz 1995b). However, the bills were more narrow than universal lustration laws and it is unclear whether an effective lustration law was in force in 1992. We decided to exclude Lithuania once we examined the spatial position of its "post-communist" parties LDLP and LSDP as reconstructed by Benoit and Laver (2006). On the scale from 1 to 20, LDLP and LSDP scored a puzzling 8.55, the result that made them look centrist rather than post-communist. For com parison, in the four countries that satisfied all our criteria, the post-communist parties scored between 1.375 and 3.57. We concluded that the conflation of the strong de-sovietization issue and lustration introduced too much noise to the measurement of party positions to make the reading of positions on lustration plausible.
The remaining four countries satisfied our criteria. For Bulgaria, Hungary, and Poland, we found two situations that satisfied the assumptions of our various empirical hypotheses with respect to the decision-making before and after the elections. Romania provided us with four cases: it was the only country in which the Post-communists twice had legislative majorities in the absence of any earlier TJ. In order to meet the model's specifications, we reconstructed for every specific case (i) the parties; (ii) their approximate positions in the TJ issue space; (iii) parliamentary procedures; (iv) PC's likely estimates of the future median; (v) the actions taken by the PC; (vi) the pre-and post-electoral distributions of seats; and (vii) the post-election changes in the TJ legislation. For all four countries, we offer brief narratives. The values of our independent and dependent variables are then summarized in Table 1

Measurement
In a model like ours, operationalization is hampered by the difficulties with the measurement of spatial locations of bills and party ideal points. Luckily, we were able to use Benoit and Laver's (2006) Party Policy in Modern Democracies (PPMD) comprehensive database. The PPMD questionnaire asked the members of parliamentary parties in post-communist Europe about their opinions on former communists. The answers were measured on a scale ranging from 1, representing "Former communist party officials should have the same rights and opportunities as other citizens to participate in public life," to 20, representing "Former communist party officials should be kept out of public life as far as possible." While the scale measures the attitudes to decommunization, we used it as a good proxy of the respondents' positions on lustration. To obtain a party's position, we averaged the scores of its members. The scale was then normalized for every country, i.e., for two or, in Romania's case, for four data points. Thus, beginning at the left-hand side of the scale, subsequent parties correspond to PC = M 1 , M 2 , ..., M n = A, and their ideal points are m 1 £ m 2 £ … £ m n . In Romania, the main post-communist party occupies the position slightly to the right of zero due to the presence of two tiny parties with post-communist or nationalist provenience. Figure 1 summarizes the key aspects of our data. Occasionally, due to party-switching, parties' seat shares fl uctuated within the same term. Acronyms are shown only in the upper panel unless the party changed its name during the term or two or more parties occupy the same spot. A party's position is shown in italics and in smaller case than the seat percentage. The heights of polygons are proportional to seat percentages. The smallest parties, small minority organizations, and independents were omitted. Country-specifi c comments: in Hungary, FiDeSz changed its name and position, and evolved from being a youth organization of SzDSz in 1996 to an independent party Fidesz-MPP in 1998 (see the case study of Hungary); in Poland and Romania, the smallest parties that are not shown occupy the extreme position of 1; in Romania, two cases are represented: 1990/92 and 1992/96. In the 1990 elections, about 20% of house seats were heavily fragmented among small parties that are not shown. Sources: Benoit and Laver (2006), Rose andMunro (2010), Millard et. al. (2002). Party positions obtained earlier were used to measure the spatial locations of bills or amendments. We assigned approximate positions to bills on the basis of our 2004 elite interviews and various state ments available in the media. For instance, we describe how in Poland the designated member of the special committee on lustration from the PSL (pre-electoral party M 3 ) highly praised the 1997 lustration law as fair while various MPs from UW (party M 4 ) publicly registered their dissatisfaction. In cases such as this, we infer that the bill was located near m 3 , the ideal point of M 3 . Also, when compar ing some of our empirical hypotheses with the corresponding propositions derived from the model, an attentive reader may notice that our empirical hypotheses require weaker measurement assumptions. For instance, Proposition 4 (h3) offers an exact prediction for the final outcome of the game, i.e., min {2m i -y, 1}, when PC chooses a bill that is too lenient for the median to accept. The corresponding H3 only states that we expect to record a new "harsher postelectoral TJ" law. Obviously, making a weaker, but still meaningful, empirical claim strengthens our case against unavoidable measurement inaccuracies.
Finally, we note various complications that we found in the data compared with the model's spec ifications. Some of them can be in all honesty disregarded while others must be discussed. For in stance, in Romania, the main post-communist party is located at a positive position, instead of at zero, since other small post-communist parties are slightly more radical. In Hungary, FiDeSz significantly changed its position between the introduction of the 1996 post-communist TJ bill and its 1998 elec toral victory. We disregarded the first problem as minor but included a longer comment on the second one.

Case studies
Below, we present brief narratives on all four countries that satisfied our assumptions C1-C3. All cases display some idiosyncrasies or small deviations from the model's assumptions. We argue below that the deviations we detected are of little significance.

Bulgaria: the median president
Our first case comes from Bulgaria and involves the 1991 elections. The postcommunist BSP won an absolute majority in the first democratic elections in postcommunist Bulgaria in 1990. It beat the anti-communist opposition bloc SDS, which was too slow to organize itself as an umbrella organization for various dissident groups. However, BSP's inability to muster support of the SDS for vital legislation quickly lead to a legislative stalemate. While SDS's support was not formally required to pass legisla tion, every bill that it opposed provoked mass protests and strikes around the country. Under duress of street politics, the BSP was forced to call early elections.
The anti-communist SDS was a frontrunner and it was fairly clear that the median would be moder ate. Uncertain was only the radicalism of the future attempts to change the lustration law. One faction of the SDS known as Dark Blue "strongly favored a rigorous decommunization program" whereas "the Light Blue faction within the SDS favored a less radical approach" (Helsinki Watch 1993).
Before we discuss the proposals of Bulgarian Post-communists made in the last months before the elections, a discussion of the legislative rules of procedure is in order. Formally the parliamentary rules of procedure were open. However, the president had the prerogative to send legislation to the Constitutional Court, which, as was commonly known, was staffed by justices closely related to the BSP. This court would strike down any reviewed lustration law. The implication was that the president had a veto over any TJ legislation, which made him institutionally equivalent to the median party. Since the president had no effective proposal power, and the legislature was expected to be mostly split between the two largest parties, the resulting setup resembled the case of closed rule. It was also certain that Zhelio Zhelev would be elected president. Zhelev was a moderate who "despite running on an SDS ticket in the presidential elections, split away from the party because of his opposition to harsh lustration laws" (Helsinki Watch 1993). Thus, we may assume that the institutional specifics of the 1991 Bulgarian political system made it equivalent to a closed-rule system with a moderate median located close to the actual median, DPS.
The post-communist actions were somewhat ambivalent. In August 1990, the BSP government was in the midst of a severe crisis, and its electoral prospects looked dim. In line with our H2, the parliament dominated by Post-communists set up a verification commission to reveal the names of secret police collaborators. However, when a few months later Georgy Tambuyev, the commission's chair, recommended publishing the names of deputies-collaborators, the same parliament opposed the idea. Indeed, in December 1990, the pre-electoral polls showed that the race between BSP and SDS was getting closer. The BSP's attempts to block the Tambuyev's commission were consistent with the intuitive expectation that when poll results improved, the Post-communists would begin gravitating towards the status quo of "no lustration." Another important factor was that the list of collaborators was surprisingly long and included 80 names, or 20% of all deputies. The lustration law was emerging as harsher than expected (Darski 1992). The attempts of Post-communists turned out to be futile once Tambuyev's list was circulated in the media. The small dose of decommunization offered by the post-communist BSP was sufficient to please Zhelev, who indeed was elected President. SDS won the parliamentary elections by a small margin, and its Dark Blue faction-in a coalition with a smaller party, the Turkish Movement for Rights and Freedoms-controlled the parliament. "They were significantly more anti-communist [than Zhelev] and were advocates for a thorough decommunization plan" (Helsinki Watch 1993). Sure enough, the Dark Blue repeatedly proposed and passed various drafts of the lustration law just after the elections in December 1991, and March, June and December 1992. However, with only one exception, President Zhelev sent these laws to the Constitutional Court, which struck them down. The post-communist legislation prevailed, thereby preventing a harsher TJ bill, in line with our H4.

Romania: déjà vu median
In Romania, two cases satisfy our criteria C2 and C3 of "Post-communists in power" and "no previous lustration law." A government dominated by Post-communists was in power before the 1992 elections. Following that, a post-communist party was the senior member in a coalition that ruled Romania until 1996. The rules of procedure were closed, with most bills originating in cabinet ministries (Ceterchi 1992). A lustration bill would be sponsored by the minister of justice.

Case 1 (1990-92):
In the founding parliamentary elections on May 20, 1990, an eclectic confed eration called the National Salvation Front (FSN) came to dominate the Romanian legislature. FSN, consolidated around ousting from power Nicolae Ceausescu, won two-thirds of the seats. Its leader and a former communist, Ion Iliescu, was elected president with 85% support. The FSN was full of "prominent former highranking communist officials, including army and Securitate officers" and "was largely controlled by a group of former communists, who wanted to reform but not change the system" (Pop-Eleches 1999). In March 1992, the FSN split into a larger post-communist FDSN led by Iliescu and a smaller anti-communist party that soon assumed the name of CDR. The resulting crisis led to early elections in September 1992.
Over the inter-election period, the Post-communists dominated the government. While the assets of the former communist party were quickly confiscated and transferred to the government, no lustration law was introduced by the postcommunist-controlled FSN. Since the post-communist FDSN was expected to win the elections by a large margin, these actions are consistent with our hypothesis H1.
In fact, the FDSN won a plurality of seats in 1992 and created a coalition with a few other minor post-communist and nationalist parties. While the FDSN came in short of a majority, its position on lustration was virtually identical with the positions of its coalitional allies (see Fig. 2 in Appendix 1). Thus, for our purposes, FDSN may be treated as a winning majority. No lustration law was introduced after the elections, in line with our H4.

Case 2 (1992-96):
The political situation changed dramatically in 1993. The anticommunist PD's rating rose significantly while the FDSN's popularity slipped (Marsh 1994). The breakdown of the ruling coalition, followed by early elections, became a realistic possibility. The FDSN changed its name to PDSR and passed a lustration law. The list of Securitate (the Romanian secret police) collaborators was released to the public and proven informers were banned from running for office. We interpret the decision of the PDSR to be in line with our hypothesis H2, that is, as a preventive move. While the coalition survived until the end of the term, in the 1996 elections, a coalition run by the CDR defeated the PDSR. In October 1997, the new government, displeased with the existing law, unsuccessfully tried to pass a harsher lustration bill through the parliament, an outcome in agreement with our H4. The preventive move of the post-communist PDSR blocked the introduction of a harsher law.

Hungary: the runaway median
In Hungary, the post-communist party MSzP won the 1994 parliamentary elections with an absolute majority of 54% of seats. To strengthen its legitimacy, the MSzP invited the Alliance of Free De mocrats (SzDSz) to join an oversized governmental coalition. The lustration law adopted earlier in 1994 was struck down by the Constitutional Court. Thus, before the 1998 elections, there was a post-communist party in power but no lustration law. The rules of procedure evolved from relatively open before 1994 to closed (Olson and Norton 1996, Olson and Crowther 2002, Bartlett 1997. Among the resolutions passed by the second parliament, 68% were initiated by the government and 24% by committees (Agh 1997).
By 1996, the ratings of the MSzP had slipped to around 20-25% while the support of its anti-communist rivals, FKgP and FiDeSz, had increased to the mid-twenties (Robinson and Marsh 1995). According to the polls, the median position was likely to go to FiDeSz, which at that time was close to the center and the SzDSz. In monthly polls conducted between January 1995 and May 1997, FiDeSz was the predicted median in every single month (Szonda 2006). While the next elections were sched uled for 1998, the post-communist MSzP could be sure to move to the opposition benches. We briefly elaborate below on how such expectation could be formed and how the 'movement of FiDeSz across the political scene' interfered with their political plans. MSzP's 54% seatshare was the result of over-representation under a mixed majoritarian electoral law (the party won only 33% of the vote) due to the pre-electoral breakup of the alliance between SzDSz and FiDeSz, which further fragmented the center-right part of the political scene. Prior to the breakup, MSzP would have needed at least 45% of the vote to win 54% of seats. In order to win a similar ma jority in 1998 elections, MSzP would have needed to increase its vote share significantly. However, MSzP's low ratings were steadily declining, in large part, as a result of the 1996 "Toksik Affair," a heavily publicized privatization scandal that involved the Postcommunists. While SzDSz was getting closer to MSzP after the latter invited it to its oversized cabinet, the Post-communists were still rel atively isolated in parliament. They had little hope to join the next governmental coalition even as a junior partner and they could reasonably expect to lose power in 1998 to anti-communist parties. In line with our hypothesis H2, they passed a new lustration law in July 1996.
The 1996 law was very mild. The number of officials to be screened was only about 600. To prove collaboration, a signed declaration of collaboration was not sufficient and had to be supplemented by evidence of collecting compensation by the agent from the secret police. Public access to secret files was severely restricted and the names of collaborators were redacted from the documents. Moreover, the screening process was scheduled to conclude by July 1997, well before the next elections. The opposition parties loudly complained about the law's impotence. Among the complainers was the future median FiDeSz, which is surprising, because its former close ally, SzDSz, seemed pleased with the bill (Halmai 1997).
While the electoral polls were returning stable predictions, the deepening rift between the two par ties that had emerged from the same dissident group was surprising. FiDeSz had originated as the youth organization of the SzDSz. FiDeSz, the acronym for "Young Democrats," had been adopted to match the SzDSz's "Free Democrats." Both parties jointly attended the Roundtable negotiations, jointly refused to sign the final version of the accords, and in November 1989, organized the referendum over the presidency, a strategic move that prevented a communist from becoming Hungary's first president. In 1994, the split between SzDSz and FiDeSz seemed like a rather inconsequential coor dination failure. However, after the elections, FiDeSz moved ideologically to the right, and changed both its rhetoric and its brand. By 1998 it had converted the spelling of its name from the capitalized FiDeSz to Fidesz-MPP, derived from Latin "fidelity," with MPP denoting "civic movement" instead of a party. It also re-wrote its mission statement, removed the age cap of 35 for its members, and moved towards nationalist and traditionalist values. As noted by an observer of Hungarian politics: "FiDeSz was a fringe youth organization kept in the shadow of SzDSz. The reason it was marginalized was because it had a radically liberal program. In the mid-nineties, almost by accident, they realized how popular they had become after some of the most liberal members left. That is when they saw the potential vote gain on the right side of the ideological spectrum. But to claim it, they had to make an ideological leap" (Interview: W 2004). Our other interview subjects, some of whom were FiDeSz politicians themselves, agreed with this assessment (Interviews: AG, GF, IH, and GK, 2004). David-Barrett et al. (2008), in a survey of lustration in Hungary, write "Fidesz had moved progressively to the right in the years before [the 1998] election and continued to do so during its term in office." The parliamentary elections were held in May 1998. As expected, the postcommunist MSzP lost and the Fidesz-MPP won both a plurality and the median position. However, it was no longer the mild centrist party it had been in 1996, proximate to the post-communist ally SzDSz. Led by Viktor Orban, who had become a staunch anti-communist, Fidesz-MPP formed a cabinet jointly with the MDF and the radical FKgP. The preventive move by the Hungarian Post-communists was insufficient to appease the runaway median. In agreement with our hypothesis H3, in November 1998, Laszlo Csucs (FKgP) handed in a draft of a new and harsher lustration law that extended the scope of lustration to persons employed in the media. A subsequent proposal prepared in the cabinet incorporated Csucs's draft and extended lustration to "members of the county and national executive or adequate corporate representatives of parties entitled to state budgetary subsidy" and to professional judges and state attorneys. The law also allowed for the voluntary lustration of lawyers, notaries, clergy and other public figures (David-Barrett et al. 2008).

Poland: the flooded median
The Polish case of 1997 and 1998 lustration laws also originated in a volatile political climate. In the 1993 elections, the victorious post-communist SLD invited another party with post-communist origins, PSL, to assume a junior position in the cabinet. The rules of procedure in the Polish Sejm were closed, with proposals originating in standing committees and the most influential figures were committee chairs Norton 1996, Olson andCrowther 2002), typically the members of the senior party in the ruling coalition. There were many earlier attempts to introduce a lustration law and one of them, in 1992, even toppled a cabinet. The resulting law passed but was not implemented. Thus, between 1993 and 1997, Poland had a postcommunist government with no working lustration law.
The power of the post-communist coalition was largely owed to the fragmentation of the post-Solidarity parties. The PR electoral law with high thresholds, the d'Hondt formula, and small districts translated a mere 20.4% of the vote for SLD and 15.4% of the vote for the PSL into 37.2% and 28.7% of seats, respectively (Kaminski et al. 1998). The Post-communists could not count on a return of two percent of seats for every one percent of votes in the next elections. In addition, by early 1997, the post-Solidarity parties were united under the umbrella of the AWS coalition. AWS' poll ratings were similar to the SLD's and hovered in the mid-twenties (OBOP 1997). While the positions on lustration of the remaining parties were somewhat scattered between those of AWS and SLD, they were overall closer politically to the AWS. Even PSL, the ideologically unstable coalition partner, purged itself of former communist politicians. SLD was unlikely to join any post-electoral coalition. In line with our H2, on April 11, 1997, the PSL-SLD-dominated parliament introduced a mild lustration law.
The Lustration Bill required that candidates for political office declare in advance whether they had collaborated with the secret political police. Those admitting collaboration were not prevented from running for office but their confession would be made available to the voters or nominating agency, possibly reducing their chances of winning the elections or nomination. Candidates denying collab oration were permitted to run unless a special Lustration Court found evidence of collaboration. The Lustration Court, with 21 justices elected by regional judiciary councils, was set to start its work by lustrating itself and other judiciary. Not surprisingly, the councils struggled with finding volunteers to serve on the lustration court. In the end, only a few high-profile collaborators were revealed (Inter views: LK 2004). The severity of lustration was further reduced by excluding from the list of lustrable offenses collaboration with military intelligence and spying on the immigrant opposition, and by the introduction of a second level of appeal in the Appellate Court.
The law intended to appease PSL, which in March and April of 1997 was the median party with respect to lustration (OBOP 1997). PSL's designated member of the special committee on lustration, Bogdan Pek, supported the 1997 bill as a fair and safe way of dealing with the past (Pek 1998). On the other hand, the politicians of the UW, also a possible median, with preferences in the TJ space to the right of PSL, publicly expressed their dissatisfaction with the 1997 law (Litynski 1998). Antoni Macierewicz of ROP, who was behind the unimplemented 1992 lustration law, called the SLD's legis lation "more of an anti-lustration law [whose] aim was to mislead the public by calling it a lustration bill" (Interviews 2004: M).
The Lustration Bill passed. It turned out, however, that the Post-communists estimated the median too optimistically. In July, just two months before the elections, Poland, along with most of Central Europe was hit with a "flood of the century." The ruling coalition was blamed for their arrogant and incompetent handling of the emergency situation and post-flood reconstruction. Subsequently, their ratings dipped (OBOP 1997). This decline was noted in the context of lustration by Jan Litynski, an The elections saw the AWS emerge as a clear winner and the UW as the median. In line with H3, the winning AWS immediately started working on a tougher lustration proposal. President Kwasniewski, close to the SLD, desperately and unsuccessfully attempted to soften or block the predicted legislation. In early 1998 the coalition of AWS and UW passed its own version of lustration law. It was still left to the AWS' ideal point but it was clearly harsher than the 1997 bill.
According to the 1998 law, lustration declarations would be verified by the Spokesman for Pub lic Interest, who would be appointed by the Supreme Court instead of the volunteer-based Lustration Court. If a statement was found inconsistent with materials from the secret police archives, the can didate would be accused of a lustration lie and tried before the Appellate Court. Only one instance of appeal was allowed. Additionally, the files of military intelligence officers and agents working for the post-transitional secret service were admitted to the lustration process. One SLD MP said that hard-line amendments had changed 70% of the statute (Dziewulski 1998). Another MP complained: "This is a record! Out of 43 articles in the lustration bill, the senate (hard-line) proposal recommends to change 31!" (Zemke 1998). MPs of all political orientations agreed that for all practical purposes the amendment was like a new bill (Interviews 2004: M).
While the post-communist preventive lustration move failed to appease the postelectoral median, it cannot be labeled "irrational." Given SLD's beliefs, which were fully compatible with electoral polls, the mild lustration was a good choice. Only the unexpected shift of voter preferences caused by harsh flood moved the median to the right. It is very likely that in the absence of any lustration law, the AWS would have been able to convince the UW to approve of an even harsher law.

Conclusion
Parties in emerging democracies strategically choose how to punish former authoritarian wrongdoers. TJ has become a political issue quite similar to taxation or budget composition and post-communist parties are active players in this game. In our paper, we presented and tested the model using data from Bulgaria, Hungary, Poland and two inter-election cases in Romania. This is an exhaustive set of all situations when the Post-communists had both an opportunity and the means to implement TJ. harsher post-electoral TJ harsher post-electoral TJ no post-electoral TJ no post-electoral TJ no post-electoral TJ full full full full full Note: "before 199x" in column CASE refers to the post-communist actions before the 199x elections; "after 199x" refers to the post-199x election outcome. Column "Fit" records the fi t of empirical case with the predictions of the corresponding empirical hypothesis. For explanation of the label "good," see the text. p-value for a one-sided binomial test: p = 0.01. Assumptions: "Full" fi t is interpreted as success; "good" fi t is interpreted conservatively as failure; the probability of a success is assumed (again, conservatively) to be 0.5 and independent within our universe of cases.
The binomial test run under conservative assumptions returned a p-value equal to 0.01. For nine cases, the empirical data are consistent with the model's predictions. In Bulgaria, where Post-communists initially introduced the lustration law but then they tried to weaken or even block it, we labelled the fit as "good." We explained their reversal by the increase in their electoral chances shown in the polls and by a surprisingly high number of revealed collaborators that made the law harsher than intended. There is no legislature in our universe of cases that produced actions clearly contradicting our predictions. This is a striking result because it shows how a general formal model can generate hypotheses capable of explaining behavior in truly diverse political settings.
Post-communist strategists can be respected for their shrewdness. In three cases out of five, their preventive action worked out precisely according to what, we believe, were their intentions. The remaining two cases cannot be considered mistakes. The overly optimistic estimates of Polish Post-communists can be fully attributed to an unexpected factor of the "flood of the century" that subtracted votes and seats from the Post-communist camp. Moreover, without the preventive move, the Polish Postcommunists would likely have suffered an even harsher TJ. What upset the preventive action of the Hungarian Post-communists was less exogenous to politics than a natural cataclysm. Nevertheless, a dramatic ideological metamorphosis of FiDeSz into Fidesz-MPP surprised both students of Hungar ian politics and scholars as well as politicians. Similarly to the Polish Post-communists, the MSzP benefited from passing soft lustration, which helped them avoid an even harsher punishment. There are various factors not accounted for in our model that are potentially relevant to the adoption of TJ. For instance, the opening of files in Bulgaria stopped the circulation of false lists of collaborators in the mass media. In Romania, the PDSR may have wanted to purge their ranks of former Securitate employees to prevent secret police agents from staging a potential coup d'etat, just as they did earlier against Ceausescu, against a legitimate democratic government. In Hungary, the MSzP may have adopted TJ as a bargaining chip with their coalition partner, the SzDSz, which felt strongly about lustration and which attempted to pass the first lustration law back in 1991. Finally, in Poland, the Post-communist bill could have helped President Kwasniewski eliminate internal party competition for his office before his bid for re-election. However, these explanations rely on the specifics of Bulgarian, Romanian, Hungarian, or Polish politics. They tell us nothing about the role of institutions in shaping the policy-making process. Various additional factors, such as the power of the Senate and other institutions, could also affect the players' preferences. However, our data back our explanation that institutions -the rules of procedure and expectations about the election results -were critical.
A less idiosyncratic competing explanation of post-communist actions relies on TJ's saliency with the electorate: Post-communists may adopt lustration bills to show to the voters that they are clear of ties to the former enforcement apparatus. However, our analysis shows the limitations of this explana tion: If it were true, Postcommunists would be adopting TJ bills irrespective of their expectations of losing power. However, as we saw in the case of Bulgaria, the post-communist lustration effort almost came to an end when the BSP started doing better in pre-electoral polls. We also saw in Romania that the post-communist actions depended on the expected outcome of the elections. Finally, and perhaps most importantly, we believe that lustration is not a salient dimension of voter choice. This stands in contrast to the politicians themselves.
Low saliency of TJ with voters is supported by evidence from a survey on TJ conducted in 2005 in Poland, Hungary and the Czech Republic (n = 3076). On average, only 22% respondents believed that former membership in the Communist Party was important in determining one's eligibility for legislative office. Other factors, such as "talents and abilities," "representing voter interests," and "be ing backed by powerful organizations" received 84%, 84%, and 59% support, respectively. Other surveys confirmed these findings (PGSW, ISP 2000). In the 2005 TJ survey respondent preferences were measured for various potentially lustrable past activities (e.g., collaboration with the ancien régime) and for various positions that could be covered by a lustration law. Although the preferences of Poles, Hungarians, and Czechs are remarkably similar, the lustration laws in these three countries differ dramatically. The Czech law covered more than 420,000 persons (5% of the popula tion) and banned from office all proven collaborators; the Hungarian law initially covered only 600 persons (about 0.005% of the population), although this number was later increased, and only revealed information about who was a proven collaborator; the Polish law covered 21,000 person (about .5% of the population) and involved a combination of both revealing information about collaborators and banning them from office (Kaminski and Nalepa 2006).
By no means is our thesis of strategic detarminants of TJ legislation limited to four countries only. The argument can be modified to those countries of East-Central Europe, where Post-communists have never won office, such as Czechoslovakia, Czech Republic, Estonia, or Slovakia. In these countries, cabinet turnovers in power involved parties created after 1989. For instance, in Czechoslovakia (and later in the Czech Republic), lustration was adopted and renewed in periods preceding turnovers be tween the neo-liberal ODS and the social democratic CSSD. In Estonia, laws revealing collaboration with the KGB were passed within two months of elections that led to a turnover in power between the Pro Patria Union and the Coalition Party. Another law was passed within three months of elections that led to the turnover between the Coalition Party and the Estonian Center Party. Finally, in Slovakia, a law opening the Institute for National Memory was passed during the last parliamentary session pre ceding the 2002 elections, in which Slovaks voted out of power a coalition made up of SDL, SOP, SDK, and SMK. Although SDL was a post-communist party, we omitted Slovakia from consideration since SDL was only a junior member of the coalition and did not hold proposal power. Moreover, Slovakia inherited a TJ bill from Czechoslovakia and its TJ status quo was much further to the right than zero.
In such post-communist countries as East Germany and post-Yugoslav republics, no TJ was intro duced by domestic actors. In Germany, the politicians from the West controlled the STASI archives and the use of materials for lustration purposes. In former Yugoslavia, the UN Security Council set up the International Criminal Tribunal for the Former Yugoslavia (ICTY). The ICTY had full author ity over prosecuting war abuses of human rights committed during the civil conflict in the Balkans. Finally, TJ in successor states of the former Soviet Union is rare, arguably because of the stronger presence of post-communist parties and politicians. Further complications arise due to the issue of "beets" and "radishes," discussed earlier in the context of Baltics.

Appendix 2
The key observation is that all main questions can effectively be reduced to PC's decision problem. Recall that a strategy of a player is SPE against strategies of other players if it plays best replies in all subgames. For some games and some strategy profiles, there may exist players with no SPE strategies. We say that a strategy x of player i admits at least one SPE strategy of player j if j has at least one SPE strategy in all strategy profiles in which i plays x. We will start with a few lemmas.
Lemma 1. For any M i , i = 2, …, n -1, the following strategy is the unique SPE strategy that admits at least one SPE strategy for A: (i) When |x -m i | = |y -m i |, minimize the distance to m i ; (ii) When |x -m i | = |y -m i | and y < x, choose x; (iii) When |x -m i | = |y -m i | and y > x, choose y.

Proof.
Since when x = y the game ends with A's move, conditions (i)-(iii) are exhaustive.
Since all subgames are last-move ones and always takes the highest payoff, it is the best reply in all subgames. It is also straightforward to check that the strategy for A defined in Lemma 2 is SPE against . To prove its uniqueness, note that every SPE strategy must satisfy (i) by definition. For (ii), let's assume that M i can choose y. Then consider the subgame H in which PC chooses y and Nature chooses M i . In H, for all 1 -x ³ e > 0, A can make its payoff equal to x -e -1 by choosing x -e, but it cannot get exactly x -1. Thus, A has no best reply in H. Hence M i 's SPE strategy that allows an SPE strategy for A must satisfy (ii). Part (iii) is proved by a similar argument. ■ Lemma 2. Let's assume that PC proposes y and every M i , for i = 2,…, n -1, plays . Then x* = min{m i + |m i -y|, 1} is an SPE strategy for A. x* is the game's outcome for all A's SPE strategies and all medians M i , for i = 1,…, n.
Proof (outline). In , M i chooses the bill closer to m i and maximizes A's payoff in case of tie. It is easy to check that, given such response, for all y, x* = min{m i + |m i -y|, 1} maximizes A's payoff at its maximal value of x* -1. Examples of other SPE strategies include, for m i £ y < 1; any action from (y, 1] or [0, 2m i -y] if 2m i -y ³ 0. In the first case, A asks for more than is feasible while in the second case, A asks for too little. In both cases, M i 's maximizing choice is . In general, since M i 's SPE strategy is unique, the choice of strategy for A determines the outcome. Since different outcomes yield different payoffs, and every SPE strategy must be payoff-maximizing in all subgames, different SPE strategies must always result in the same outcome. Finally, when the median is PC or A, by definition x* = y or 1, respectively. ■ By Lemmas 1 and 2, there exists a profile of SPE strategies for M i and A. Every such a profile must result in the same outcome x* (y) for any given SPE strategy y of PC and move of Nature. Thus, when x* and are played, strategy y of PC determines the outcomes given the move of Nature M i , and we can define the SPE payoff resulting from y as P*(y). The problem of PC becomes the one of maximizing its payoff in face of uncertainty associated with the choice of the median. Since PC is risk-neutral, its total expected payoff from y is the sum of partial payoffs (y) for different medians chosen by Nature:

Lemma 3.
, where: Proof. The term (y) represents the PC's partial payoff from playing y when the median is M i . One of three cases holds: m i is closer to 1 than to y; m i is no farther from y than from 1 and y is smaller than m i ; y is no smaller than m i . Note that the first condition in the definition of , y < 2m i -1, is satisfied only for rightist medians, i.e., when m i > 1/2; the second condition is satisfied for all medians except 0. ■ We may re-write Lemma 3 in a more convenient form, using appropriately defined indexes. For any y, let l(y) denote the largest index of a party with the position to the left, or exactly on y, i.e., such that m l(y) £ y < m 1(y) + 1 . Let r(y) be the largest index of a party that is closer to the right to y than to 1, i.e., such that m r(y) Î (y, + y) but m r(y) + 1 Ï (y, + y).

Proposition 3.
The formula in Proposition 3 follows directly from Lemma 3. It divides PC's payoff into three components. When for some y the summation in the last two components runs over an empty set of indexes, e.g., for y = 1, we assume a convention that the entire sum is zero.
Proof of Proposition 2. Ad (i): Strategies x* and from Lemmas 1 and 2 satisfy the conditions of SPE strategies for A and all M i -s, respectively, i.e., they are best replies in all subgames. We need to prove that PC has at least one SPE strategy as well. Such existence follows from the fact that the total payoff of PC, P*, is a convex combination of partial payoffs , as shown in Lemma 3. Since all -s are continuous over [0,1], their convex combination is continuous as well and, since [0,1] is compact in the usual topology, it has a non-empty and closed set of global maxima. Any such maximum is an SPE for PC. Decyzje  Ad (ii): For i = 1,…, n, every is piece-wise linear over intervals with the endpoints consisting of m i and, possibly, 2m i -1, and has its maximum at m i . Thus, as a convex combination of -s, P* is piece-wise linear as well with its set of endpoints being the subset of all endpoints of all -s. Consequently, P* must have maxima within the set of its endpoints. No point of the form 2m i -1 can be a (local or global) maximum unless it coincides to some endpoint m j since the left-hand-side derivative of P* is greater than the right-hand-side derivative at 2m i -1 while the derivatives of the other components of the sum are constant in the neighborhood of 2m i -1. Informally, function P* cannot simultaneously be increasing on the left-hand side of 2m -1 and decreasing on its right-hand side. This means that there must be a maximum among the mi-s and, since P*(1) = -1 is the minimal possible payoff, it must be within {m i } i = 1,…, n -1 .
Moreover, any point between two adjacent endpoints of a piece-wise linear function maximizes it iff the endpoints maximize it as well. Since no point 2m i -1 can be a maximum, the adjacent endpoints must come from {m i } i = 1,…, n -1 .
Ad (iii) (outlined): The model with n players is a set S parametrized by n -2 bliss points and n probabilities. It is a Cartesian product of a (n -2) dimensional set defined by inequalities 0 < m 2 < … < m n-1 < 1 and an (n -1)-dimensional simplex defined by inequalities 0 £ p i £ 1 and a constraint . Thus, S is a (2n -3)-dimensional convex subset of a (2n -3)-dimensional Euclidean space.
For each game with multiple equilibria, (ii) implies that for at least two bliss points m i ¹ m j P*(m i ) = P*(m j ). By Lemma 3, this equality imposes an additional constraint on the subspace S i,j of games that have m i and m j among their SPE. Since m i ¹ m j , the equality defining S i;j is different than . Thus, S i,j must be of a dimension no higher than 2n -4 and it is generically nonexistent in S. The total number of spaces indexed by different pairs i and j is finite, namely, n(n -1). Their topological union, È i ¹ j S i,j , is also generically nonexistent in S. ■ Proposition 3 combined with Proposition 2 (ii) simplify the calculation of equilibrium strategies. We need to calculate PC's payoffs only for all bliss points and select the ones that maximize it along with, possibly, intervals connecting adjacent maximizing endpoints.
The next Proposition states the formal versions of empirical hypotheses H1-H4. Let's denote by k the index of the most rightist left-center party, i.e., such that m k £ 1/2 but m k + 1 > 1/2. Let's assume for simplicity that m 2 > 0, i.e., that no other party shares its ideal point with PC. The results can be easily generalized when more parties' ideal points are located at 0.