2. Interpersonal influence in legislatures and beyond

It should come as no surprise that legislators speak of being influenced by fellow legislators nor that they take cues from these members. Legislators face a host of issues and are called upon to vote hundreds of times each year, making it impossible for any individual to stay fully apprised of all the matters that will come before them. The complexity of the policymaking process, and the attendant uncertainty, is one reason for the existence of institutionalized committees that foster expertise and informative signaling (Krehbiel, Reference Krehbiel1991). In his influential work on roll-call voting in Congress, Kingdon (Reference Kingdon1989) argues that committee experts are integral sources of information for uncertain legislators (see also Box-Steffensmeier et al., Reference Box-Steffensmeier, Ryan and Sokhey2015). Co-partisans, state delegation colleagues, and party leaders also provide cues about how to vote, particularly on less salient issues (Matthews and Stimson, Reference Matthews and Stimson1975; Kingdon, Reference Kingdon1989).

Beyond the “professional sources” (experts, co-partisans, and members with similar district or state constituencies) emphasized by these studies, scholars have also argued that an important factor in legislative decision making is much more personal in nature, consistent with the statements by Menendez and Biden. That is, the interpersonal relationships among legislators and the networks in which members are embedded are likely to affect the choices they make. Political scientists have recognized this for some time. In his classic work on the antebellum Congress, Young (Reference Young1966) identifies congressional boarding houses as a key source of legislative networking that produced unique voting blocs in Congress (but see Bogue and Marlaire, Reference Bogue and Marlaire1975). Minozzi and Caldeira (Reference Minozzi and Caldeira2021) re-examine living arrangements in the 19th century US House of Representatives and provide an exhaustive analysis spanning 60 years that takes great pains to carefully identify proximity effects.

In a related vein of research, Patterson (Reference Patterson1959) and his collaborators examine the patterns and implications of interpersonal networks in the Iowa and Wisconsin legislatures. Caldeira and Patterson (Reference Caldeira and Patterson1988) argue that friendship and respect are key sources of legislative initiative and action. In other work, Caldeira and Patterson (Reference Caldeira and Patterson1987) consider three sources of friendship ties in the legislative context: homophily (that like-minded members are naturally drawn together), shared attributes, and spatial proximity. As they note, “seating arrangements are not mere housekeeping items for legislatures; on the contrary, they have a good deal to do with the nature of social relationships and the cohesion of parties within the legislature” (969). They find that the most significant proximity effect accrued among deskmates, as legislators were much more likely to identify the legislator with whom they shared a desk as a friend than they were non-deskmates. Also in this spatial vein, Patterson (Reference Patterson1972) uncovers a link between seating and party cohesion in Congress by tracing partisan seating in the US House and Senate from the Civil War through the first decade of the 20th century. Concurrent with the well-known rise in polarization over that time span, legislators in both chambers adopted a greater degree of intra-party seating cohesion by the turn of the century. While Patterson's aggregate-level account is suggestive of a link between seating and voting behavior, the causal mechanism is not clearly specified or assessed.

More recently, Masket (Reference Masket2008) examines the effect of being deskmates on agreement scores in the California Assembly from 1941 to 1975 and finds a consistent positive relationship between seating proximity and similarity in voting. In their study of network effects in congressional voting, Cohen and Malloy (Reference Cohen and Malloy2014) examine seating proximity in the Senate as one among many indicators of interpersonal connectivity in the 101st to 110th Congresses (1989–2008). While most concerned with the effect of alumni networks and politicians’ links to industry, they, like Masket, find a positive effect of proximity on roll-call voting similarity in their analysis.

In a particularly innovative study, Rogowski and Sinclair (Reference Rogowski and Sinclair2012) employ the US House office lottery to examine the effects of House office location on legislative behavior. At the beginning of each Congress, new members draw numbers in the House office lottery and subsequently pick their office locations from the remaining available locations in the order drawn in the lottery. Thus, members who randomly draw lower numbers in the lottery are able to choose from a broader set of available offices than those drawing higher numbers. Using these randomly drawn lottery numbers as an instrumental variable, Rogowski and Sinclair find that House office proximity does not influence legislative behavior. Ferber and Pugliese (Reference Ferber and Pugliese2000) likewise find that proximity in office location has no effect on communication patterns in the New York State Assembly. And while finding that seating proximity on the floor is positively related to communication, they conclude that much of this proximity effect is due to homophily.Footnote ⁶

Importantly, none of these studies employs a fully randomized set of seat assignments and thus none can identify whether any effects of spatial proximity on legislative behavior are due to behavioral diffusion or homophily. For example, the Speaker in the California Assembly chooses where members sit (Masket, Reference Masket2008: 304). In the sessions of the US Congress examined by Cohen and Malloy (Reference Cohen and Malloy2014), senators choose by class where to sit, affording extensive opportunities for homophily to drive similarity in floor behavior. Although the Wisconsin and Iowa legislatures examined by Caldeira and Patterson (Reference Caldeira and Patterson1988) employed lotteries, neither resulted in a random set of seat locations. Rather, these lotteries induced a constrained choice process, with members drawing lottery numbers but then being free to select their seats from those still available. Members had ample opportunities to choose to sit next to friends, particularly those who drew lower lottery numbers. This lottery process is identical to the House office lottery examined by Rogowski and Sinclair (Reference Rogowski and Sinclair2012). Thus, while these studies examined whether spatial proximity influences legislative behavior, lacking a random seating assignment mechanism, none is able to identify fully whether proximity effects reflect behavioral diffusion or homophily.

Although studies of random seating assignment are almost non-existent in the legislative politics literature, there has been considerable interest in other disciplines in random spatial assignments. These studies, like ours, are motivated by the identification problem inherent in identifying how spatial proximity affects behaviors of various types. Distinguishing between direct behavioral influence among neighbors versus homophily is impossible without knowing how actors are selected into their spatial locations (see Manski, Reference Manski1993). One particularly rich literature on peer effects examines dormitories. These studies exploit the random assignment of students in college dormitories to examine how spatial proximity influences behaviors and outcomes both in college and in subjects’ career paths. These studies find that spatial proximity to randomly assigned neighbors influences students’ grade point averages and decisions to join social organizations such as fraternities (Sacerdote, Reference Sacerdote2001), employment outcomes (Marmaros and Sacerdote, Reference Marmaros and Sacerdote2002), racial attitudes (Shook and Fazio, Reference Shook and Fazio2008), and interracial friendships (Baker et al., Reference Baker, Mayer and Puller2011). In short, while there is substantial evidence that randomly assigned spatial proximity influences a variety of behaviors, we do not know whether such effects extend to political elites. Nor do we know whether they extend to expressly political behaviors, such as legislative voting behavior.

3. Alþingi

Founded in 930, Iceland's Alþingi is the oldest existing parliament in the world. A unicameral legislature since 1991, Alþingi currently has 63 members, although this includes nine to twelve cabinet ministers and the speaker, who usually are MPs. The MPs sit in a hemicycle with cabinet ministers and the speaker sitting in specially designated seats in front of the chamber, see Figure 1.Footnote ⁷ While formally a semi-presidential system, Iceland has functioned as a “normal” parliamentary system for the most part since gaining independence in 1944. Government coalitions are the norm, the government has a fairly firm hand on the legislative agenda, and party discipline is high. MPs can propose legislation, but, as in most parliamentary systems, the success rate of private member bills is low. Overall, legislative politics are dominated by the political parties and Alþingi's weakness and lack of independence are often bemoaned by MPs—particularly when they find themselves in the opposition.

Figure 1. Alþingi seating chart (119th session).

The Icelandic party system can be described as having a core of four major parties whose roots extend back to the beginning of the republic, although some of them have merged with other parties and suffered from splits. We provide an overview of the parties and coalitions as well as a representative look at our multidimensional scaling of the voting record in Appendix A of the Supporting Information (SI).

3.2 Session and legislative mechanics organization

The electoral term is four years and is split into four legislative sessions with the addition of the occasional short summer session that typically follows elections. Alþingi convenes for a new session at the beginning of October each year and the session runs for about eight or nine months, with business concluded around mid-June—the exception being election years, when the session usually ends in late April (Indridason and Kristinsson, Reference Indridason and Kristinsson2018a). MPs spend a considerable amount of time on the floor. Between 2005 and 2010, the chamber convened for between 490 and 886 hours per legislative session.Footnote ¹⁰ This amounts to meetings being in session for about 15–25 hours per week during the legislative session. Of course, this does not mean that all the MPs are present in the chamber for the whole time.

Legislative proposals in Alþingi undergo three debates. The first debate addresses the bill as a whole and, following the debate, the bill is referred to committee. No vote is taken unless requested by an MP or if there are multiple proposals over the committee of referral. During the second debate, votes are taken on individual sections of the bill as well as amendments. The bill may be referred back to committee if amended. In the third debate, votes are taken on amendments and amended sections as well as on the bill as a whole as amended. The speaker determines how votes are taken, that is, the speaker may, for example, bundle multiple sections of a bill together rather than taking separate votes on each section of the bill. The speaker's decision can be overruled by parliament at the request of a parliamentary party or nine MPs. Parliamentary motions follow a similar procedure. The speaker decides how votes are taken. The speaker can forgo a vote when he or she is confident that there is unanimous consent or a clear majority in Alþingi and if no MP raises an objection. The exception is final votes where a vote must be taken. Votes are recorded electronically—unless there is a malfunction in which case votes are taken by a show of hands. The speaker can, and must if requested by any MP, conduct a proper roll call.

The number of bills and parliamentary motions proposed during the 119th–144th sessions (1991–2015) are shown in Figure 2. In this period, Alþingi considered, on average, 219 bills and 122 parliamentary motions during a regular parliamentary session. The average number of votes taken during those same sessions (shown in Figure 3) was 1,430 with over 2,000 votes taken during a couple of sessions. The great majority of votes are conducted electronically and the votes proceed fairly quickly. For example, Alþingi's yearly report for the 139th session notes that voting took 32 hours, which means each vote required less than a minute and a half on average.Footnote ¹¹

Figure 2. Number of bills and motions per session.

Figure 3. Number of votes per session.

The great majority of legislative proposals are government bills introduced by cabinet ministers. Between 1991 and 2016, 68.4 percent of all bills were government bills, followed by opposition MPs introducing about 20.3 percent, and government MPs accounting for the bulk of the rest.Footnote ¹² All bills are referred to committee after first reading. Although private member bills account for a fair share of introduced legislation, private member bills are less likely to make it out of committee and are, thus, less likely to be voted on and adopted. Legislative proposals expire at the end of the term and must, therefore, be re-introduced in the following session for continued consideration. In the same time period, opposition MPs introduced 45.5 percent of all parliamentary motions, government MPs introduced 32 percent, and government ministers 22.5 percent.

4. Spatial analysis

With this information about Alþingi in hand, we now turn to the diagnosis and modeling of spatial dependence in peer effects in roll-call voting. If legislators’ seating location predicts their roll-call voting behavior, the result is spatial autocorrelation, or spatial dependence.Footnote ¹³ Formally, spatial dependence refers to a non-zero covariance between the values on a random variable for neighboring units:

(1)$$\rm{Cov}( y_{i},\; y_{\,j}) = E( y_{i}y_{\,j}) - E( y_{i}) E( y_{\,j}) \neq 0 \rm{~for~} i \neq j,\; $$

where i and j denote spatial locations (Anselin and Bera, Reference Anselin and Bera1998: 241–42). Positive spatial autocorrelation exists when neighboring units (e.g., legislators) have similar values on the random variable while negative spatial autocorrelation exists when neighboring units have dissimilar values on the random variable. In our application, we focus on positive spatial dependence because we are interested in identifying whether the similarity in voting behavior of neighboring legislators found in previous studies is due to behavioral diffusion. Positive spatial dependence exists if neighboring members of Alþingi exhibit greater similarity in roll-call voting behavior than would be expected by chance.

4.1 Spatial dependence

The first step in diagnosing spatial dependence in members’ roll-call voting behavior is to estimate this dependence in the absence of covariates. Tests for spatial dependence have been developed for both the global and local levels (see, e.g., Darmofal, Reference Darmofal2015). Tests for global spatial dependence diagnose whether the data as a whole exhibit spatial dependence, while local tests diagnose which units (members in our analysis) exhibit spatial dependence. Thus, in our application, a test for global spatial dependence would examine whether legislators as a whole exhibit spatial autocorrelation on a particular roll-call voting measure in an Alþingi session. The principal test for global spatial autocorrelation, and the one we employ in this article, is the global Moran's I. The global Moran's I test is:

(2)$$I = {N\over S}{\Sigma_i \Sigma_j w_{ij}( y_i - \overline{y}) ( y_j - \overline{y}) \over \Sigma_i ( y_i - \overline{y}) ^2},\; $$

with N denoting the number of observations, S the sum of the weights, w _ij an element of the spatial weights matrix W, y _i and y _j the values on the random variable at locations i and j, and $\overline {y}$ the mean of y.

A key component of Moran's I is the spatial weights matrix. This weights matrix denotes which units are to be treated as neighbors of each other and which are to be treated as non-neighbors. This is a critical decision, as only neighbors of unit i are allowed to exhibit first-order spatial autocorrelation with unit i (non-neighbors exhibit only higher-order dependence with i, through neighbors of neighbors). In the weights matrix, neighbors of unit i have non-zero values, non-neighbors of i have zero values, and, typically (as in our analysis), i is treated as a non-neighbor of herself.

We consider three definitions of spatial proximity between members of Alþingi (depicted in Figure 4). The first is an adjacent neighbor definition, in which only legislators who sit on either side of legislator i are considered neighbors of i. The second is a rook neighbor definition, in which members sitting directly in front of or directly behind legislator i are added to the adjacent neighbor definition and are also considered neighbors of i. Our final neighbor definition is a queen neighbor definition, in which members who are sitting to the left or right diagonally in front of or behind legislator i are added to the rook neighbor definition. In other words, the queen contiguity neighbor definition is the most comprehensive of the neighbor definitions and is one in which all legislators surrounding i are treated as neighbors of i.

Figure 4. Neighboring locations.

A positive and significant global Moran's I indicates positive spatial dependence. High values cluster with high values at neighboring locations and low values with low values. In our analysis, this would mean, for example, that neighboring members of Alþingi exhibit more similarly liberal (or conservative) voting records than we would expect by chance.

If spatial dependence is diagnosed at the global level, the next step is to examine local spatial dependence to identify which units are spatially autocorrelated with their neighbors and which are spatially independent. Such local spatial dependence can be examined via the local Moran's I. This local Moran's test is a member of a class of statistics known as local indicators of spatial association (LISA) statistics. LISA statistics are tests for local spatial dependence that meet two conditions: (1) they identify which units are autocorrelated with their neighbors and (2) their sum is proportional to a corresponding global measure (Anselin, Reference Anselin1995). The use of the local Moran's I in connection with the global Moran's I allows us to disaggregate the global measure by identifying which units are producing the global finding and which exhibit spatial randomness.

The local Moran's I takes the following form:

(3)$$I_i = {\Sigma_j w_{ij}( y_i - \overline{y}) ( y_j - \overline{y}) \over ( y_i - \overline{y}) ^2},$$

where the notation is identical to that presented for the global Moran's I. A key distinction between the local and global Moran's I tests is that in the former, only the neighbors of i are incorporated in the estimates at each location while in the latter summation occurs over all i.

4.2 Modeling spatial dependence

The tests discussed thus far diagnose spatial dependence at the global and local levels in the absence of covariates. We also, however, want to model peer effects controlling for members’ parties, to determine whether any behavioral influence between neighboring legislators persists in models that account for co-partisans sitting next to each other. Behavioral diffusion, or peer effects, between neighboring legislators are consistent with a spatial lag model that captures the diffusion of behavior between members. Such a model takes the form:

(4)$$y = \rho Wy + X\beta + \varepsilon,\; $$

where y is an N by 1 vector of observations on the dependent variable, Wy is a spatially lagged dependent variable with a spatial weights matrix W, X is an N by K matrix of observations on covariates, β is a K by 1 vector of parameters, ρ is the spatial autoregressive parameter for a spatially lagged dependent variable, and $\varepsilon$ is an N by 1 vector of error terms. The key component of the spatial lag model that sets it apart from non-spatial models is the spatially lagged dependent variable Wy and its corresponding spatial autoregressive parameter, ρ. A positive and significant ρ parameter indicates positive spatial diffusion in which members influence each other to vote similarly. A negative and significant ρ parameter indicates negative spatial autocorrelation in which members’ interactions lead them to vote dissimilarly from each other. And a ρ parameter that is indistinguishable from zero indicates the absence of behavioral diffusion between members.

At first glance, the spatial lag model bears some surface similarities to a temporally lagged dependent variable in time-series analyses. This surface similarity, however, is misleading, as influence flows in only one direction in time-series analyses, from the past to the present, while the spatially lagged dependent variable captures simultaneous spatial dependence. In our application, member i influences her neighbors’ voting behavior while her neighbors also simultaneously influence i's behavior. Indeed, this simultaneous spatial influence is intrinsic to peer effects. But to the best of our knowledge, ours is the first analysis to model this simultaneity in the context of a random seating assignment.

Because of the simultaneity in the peer influences, ordinary least squares (OLS) is a biased and inconsistent estimator of ρ and thus should not be employed to estimate the value of ρ. Instead, maximum-likelihood estimation (ML) that accounts for the simultaneity is typically employed to estimate ρ (see, e.g., Darmofal, Reference Darmofal2015). As Anselin and Bera, Reference Anselin and Bera1998: 256) show (see also Anselin, Reference Anselin1988: 181–82), the ML estimates for β and σ ² are:

(5)$$\beta_{ML} = ( X'X) ^{-1} X'( I - \rho W) y$$

and

(6)$$\sigma_{ML}^{2} = {( y - \rho Wy - X\beta_{ML}) '( y - \rho Wy - X\beta_{ML}) \over n}.$$

Conditional upon the spatial autoregressive parameter, ρ, the estimates for these non-spatial components are simply the OLS estimates applied to a spatially filtered dependent variable, (I − ρW)y, that is, a dependent variable with the effect of the spatial autocorrelation removed, and the covariates (Anselin and Bera, Reference Anselin and Bera1998: 248, 256). Substituting these two sets of ML estimates into the log-likelihood function then produces a concentrated log-likelihood function of the spatial autoregressive parameter, ρ:

(7)$$L_{Lag}^c = -{n\over 2}\rm{ln}\left[{( e_{O} - \rho e_{L}) '( e_{O} - \rho e_{L}) \over n}\right] + \sum_{i}\rm{ln}( 1 - \rho\omega_{i}) ,\; $$

where e _O and e _L are, respectively, the residuals from OLS regressions of y on X and from W _y on X (Anselin, Reference Anselin1988: 181). The ML estimate of ρ is then found from the optimization of this concentrated log-likelihood function (Anselin and Bera, Reference Anselin and Bera1998: 256). We employ this ML estimator using the concentrated-likelihood approach for the spatial lag models in our analyses.

5. Data

To our knowledge, votes in the Icelandic Alþingi have not been scaled previously using contemporary political science approaches. Kristinsson (Reference Kristinsson2011) examined party cohesion from 1961 to 2010, noting high levels of both unanimity and party unity, particularly in the period since 1991 that coincides with the introduction of electronic voting and the shift to a unicameral legislature. Kristinsson's findings with respect to party cohesion, as well as the frequency with which many matters are disposed of unanimously, are consistent with legislative voting in parliaments more broadly.

The lack of variation in voting within parties and across Alþingi as a whole poses some potential challenges for us. First, scaling techniques such as NOMINATE rely on non-unanimous votes for estimation. Second, to the degree that votes do not capture underlying variation in preferences due to selection effects inherent in the roll-call record, we may not be obtaining true measures of legislator preferences (Carrubba et al., Reference Carrubba, Gabel, Murrah, Clough, Montgomery and Schambach2006). In some senses, then, voting in a highly partisan parliamentary system like Alþingi presents a higher hurdle for uncovering evidence of proximity effects in legislative voting.

We examine a number of dependent variables that summarize legislative voting for individual sessions of Alþingi. As described above, the number of votes cast is often well over 1,000, although in shorter sessions there can be considerably fewer votes. Since many votes are unanimous, the scoring of the votes is based on smaller subsets of votes.

Our first measure is the Coalition Support Score, defined as follows. Votes on which a majority of voting MPs in the governing coalition voted in opposition to a majority of voting members outside the governing coalition are identified as coalition votes. Thus for MP_i across coalition votes j:

(8)$${{\it Coalition \;Support\; Score}}_i = 100 \times {\#( {{\it Votes \;with \;Coalition}}) \over {\# ( {\it Coalition \;Votes}) }}.$$

This measure varies in line with the degree of support an MP demonstrates for the coalition and ranges from 0 to 100. As a practical matter, it is “lumpy” at both ends of the distribution, with opposition MPs typically having scores close to 0 and those in the government with scores at or approaching 100.Footnote ¹⁴

The second measure is the Party Defection Rate, which is similar to the Coalition Support Score but simply defined in terms of party rather than coalition support. As such, it gives us a window into a different behavior that might be tied to seat proximity—the likelihood of defection from one's party. Here we identify a party position for all votes within each party on which a majority of its voting members were decisive (i.e., not tied). A defection occurs when an individual MP votes in opposition to the party's position. As such, for MP_i across party votes j:

(9)$${{\it Party \;Defection \;Rate}}_i = 100 \times {\#( {{\it Defection \;Votes}}) \over {\#( {\it Party \;Votes}) }}.$$

Not surprisingly, defection rates tend to be quite low. Yet there is some variation, albeit less than what we observe in coalition support.Footnote ¹⁵

In addition to these more conventional voting scores, we estimate both WNOMINATE and IDEAL scores in order to obtain indicators of legislator ideal points. The WNOMINATE approach is grounded in the spatial theory of voting and was developed by Poole and Rosenthal (Reference Poole and Rosenthal1997). It assumes a Gaussian distribution for the deterministic component of a legislator's utility function, and is ubiquitous in studies of the US Congress. WNOMINATE allows researchers to generate estimates of legislative preferences that often neatly summarize hundreds of votes or more with a simple indicator based on a single dimension of public policy conflict. For much of US history, a second issue dimension involving racial politics captured some of the remaining variation not picked up in the first dimension of liberal-conservative division over economic issues. Another attractive feature of WNOMINATE is that analysts simply need to fix the polarity of one legislator per dimension estimated in order to orient the policy space. In the analyses presented here, we have estimated WNOMINATE scores on two dimensions for each session of the Alþingi with more than 20 non-unanimous votes. A large proportion of the variation is picked up by the conventional socio-economic left–right dimension. A second dimension, significantly less predictive though still relevant in most sessions, seems to involve a rural–urban divide. On the latter, it is frequently the case that Social Democrats, whose strength lies in urban areas, appear distinct from the Left-Greens, whose roots are more rural and tend to emphasize issues involving the environment and sustainability.Footnote ¹⁶

In recent years, methodological advances have led to the increased use of Bayesian approaches to ideal point estimation. Clinton et al. (Reference Clinton, Jackman and Rivers2004), among others, advocate moving away from the classical (or frequentist) approach to scaling legislative voting due to the implicit assumptions embodied in these models. More specifically, the Clinton, Jackman, and Rivers (CJR) approach adopts models based on item response theory (IRT) to uncover estimates of legislator ideal points (IDEAL) that are based on a different parameterization of the utility function, which in this case is quadratic. An advantage of this model is its greater flexibility in contexts in which WNOMINATE will not function, for example, few votes with a small number of legislators. Moreover, it allows scholars to incorporate additional information about the context involving the substance of issues and/or the underlying preferences of legislators.Footnote ¹⁷ We find that in most cases, the first dimension scores returned by both WNOMINATE and IDEAL are highly correlated with one another, although as previous work has noted (Carroll et al., Reference Carroll, Lewis, Lo, Poole and Rosenthal2009; Clinton and Jackman, Reference Clinton and Jackman2009), the IRT approach of CJR seems to be more sensitive to extreme or outlying cases. We are agnostic on which of the two approaches to scaling is preferable, and employ both in our analyses for the sake of completeness.