Crossing the Line: Evidence for the Categorization Theory of Spatial Voting

Abstract Bølstad and Dinas (2017) propose a model of spatial voting, based on social identity theory, that suggests supporting a candidate/policy on the other side of the ideological spectrum has a disutility that is not accounted for by common spatial models. Unfortunately, the data they use cannot speak directly to whether the disutility arises because individuals perceive their ideology as a social identity. We present the results of an experimental study that measures the norm against crossing the ideological spectrum; tests the cost of doing so, controlling for spatial effects; and demonstrates that this cost increases with the salience and strength of identity norms. By demonstrating the norm mechanism for the disutility of crossing the ideological spectrum, we provide strong support for B&D's model.

the same and opposite sides of the ideological spectrum as the respondent are clearly in different spatial positions.On the coarse ideological scale used, the difference between being on the same and opposite side of the ideological spectrum is at least 1/5 of its range (or more, depending on where the respondent places the parties).This confounds the effects of distance with the effects of crossing the centre.B&D provide compelling evidence of discontinuities in voters' party preferences at the centre of the ideological spectrum for a variety of voter self-placements and show that the effects of the centre on party preferences persist even when comparisons are restricted to parties at an equal ideological distance from the voter.Yet, B&D are unable to completely rule out the possibility that the discontinuity at the centre of the ideological spectrum is an artefact of some yet unknown distance function, as unlikely as that may seem.
Further, and more importantly, while their evidence is consistent with the categorization theory and highly persuasive, B&D cannot speak directly to whether this effect arises because individuals perceive their ideology as a social identity.We thus aim to augment their categorization theory by pinning down the mechanism through which the disutility of 'crossing the centre' arises: norms associated with an ideological identity.By their membership in an ideological identity group, people know that others expect them to follow a set of norms about which candidates/ policies they should and should not support.They suffer social and psychological costs from violating norms and thus are disinclined to do so.Hence, the discontinuity is generated by the most basic ideological group normdo not support the other side.
To assess the validity of this interpretation of categorization theory, our experimental study: measures the norm against crossing the ideological centre; tests the cost of doing so, controlling for spatial effects; and demonstrates that this cost increases with the salience and strength of identity norms.The resulting contribution extends beyond the literature on vote choice.By showing how norms shape individuals' assessments of those with an opposing ideological identity, we contribute to the literature on affective polarization (Mason 2018), which has suggested but not tested the idea that political identity norms contribute to polarization (Iyengar and Westwood  2015).Our findings also have potential implications for another voting theorythe reputational premium theory (Sniderman and Stiglitz 2012)which we discuss in the concluding section. 2

A Categorization Theory of Voting
The categorization theory of spatial voting postulates that voters think in terms of ideological categoriesleft versus right, conservative versus liberaland do so because an ideology can be a social identity (Bølstad and Dinas 2017).However, categorization theory does not offer an explicit account of how such identities influence behaviours and attitudes.We offer an interpretation of the categorization theory that builds on recent work arguing that identities matter for behaviour because of the norms associated with them (Groenendyk, Kimbrough, and Pickup 2022; Klar  2013; Pickup, Kimbrough, and de Rooij 2022).By norms, we mean shared expectations about how group members ought to behave by virtue of their group membership.We argue that a concern for following group norms influences decisions alongside personal preferences regarding the candidate/policy.This yields a model in which utility depends on both personal preferences and adherence to group norms, which is reminiscent of models of vote choice by Fiorina (1976), Jessee (2012), and Sniderman and Stiglitz (2012). 3ur model has two parts.The first captures the individual's personal preferences, including personal policy preferences.Here, the payoff an individual receives from supporting a particular 2 Another alternative to the categorization theory is cognitive dissonance (Festinger 1957).It is possible that voting for a party on the other side of the ideological spectrum gives rise to disutility via cognitive dissonance.That said, our findings suggest the source of that cognitive dissonancethe violation of a norm that originates in a political identity.In other words, if it is norms that drive the categorization effect, this theory may not be so different from that of cognitive dissonance.candidate/policy is a function of the distance between the position of their personal ideal candidate/policy and the position of the candidate/policy in some policy space.The model can accommodate many ways of defining this space (and the distance metric), which need not be restricted to a single dimension.For example, the proximity model uses the simplest metric --the distance between a person's ideal candidate/policy and an actual candidate/policy on a left-right spectrum (Downs 1957).In evaluating alternatives, the payoff an individual receives from a candidate winning or a policy being implemented is weighted by the probability that the candidate/policy wins or is implemented (given that the individual supported the candidate/policy).The difference between this payoff and the payoff the individual receives from the candidate/policy not winning or not being implemented captures the personal considerations at stake when voting.
So far, the model is a classic spatial model with voters with well-defined preferences over policies/candidates (Downs 1957; Enelow and Hinich 1984).The model is augmented by assuming individuals also have preferences about norms, preferring (all else equal) to follow their identity groups' norms.We understand the influence of identities via the social and psychological consequences of experiencing or imagining the (dis)approval of other group members.The second part of the model thus considers the degree of disapproval group members expect to receive from violating a particular norm; this is the norm strength (Bicchieri 2006).However, a norm of a given strength may still affect two group members differently depending on the norm's salience (Ybarra  and Trafimow 1998); that is, whether it is 'top of mind'.For example, political advertising may make the norms of one member's political identities more salient.
While normative considerations associated with any social identity may enter the voting model, our experiment exploits the intuition that ideological identity creates a discontinuity at the centre of the ideological spectrum, as implied by the categorization theory.If a candidate/policy is on the same side as the individual, support for that candidate/policy is likely consistent with ideological group norms (support those on 'your side').If a candidate/policy is on the opposite side of the individual, support for that candidate/policy is likely inconsistent with ideological group norms (don't support the 'other side'). 4Our first contribution is to provide empirical verification of this intuition by measuring the strength of the norm against supporting policies/candidates from the other side of the ideological spectrum.We next demonstrate that the perceived cost of violating this norm affects reported vote preference, controlling for spatial considerations.
We then use another intuition from the model to demonstrate that the cost of violating ideological identity norms increases with the salience and strength of the norm.The intuition is that individuals can experience a conflict between their personal preferences and the norms of their ideological identity (or any politically relevant identity).For example, a small business owner may have preferences regarding the minimum wage that do not align with their liberal identity.We use response times to measure the conflict experienced by individuals when they express a personal preference inconsistent with the norms of their ideological identity.This conflict reflects the cost of violating the norms, and we use a priming manipulation to show that increasing the salience of such norms increases the conflict individuals experience.We also demonstrate that this effect is greater for those who perceive the norm as stronger.
Experimental Design -Part 1 Our two-part experiment was included in a survey we commissioned from YouGov in Britain and the United States.Sample sizes are 3,219 and 3,000, respectively. 5The first question (Q1) asks respondents to place themselves on a 0 to 100 ideological scale. 6The remainder of our survey excluded those that placed themselves in the centre of the spectrum (11 per cent of British and 12 per cent of American respondents) and those who did not identify themselves on the ideological spectrum (19 per cent of British and 10 per cent of American respondents). 7he second question (Q2) displays the respondent's self-placement on the ideological scale from Q1 and the position of two hypothetical parties: A and B. Party B is randomly placed either 0.5 units just left of centre or 0.5 units just right of centre.The randomization divides respondents into two groups.In the control group, party B is on the same side of the ideological spectrum as the respondent but only 0.5 units away from the centre.In the treatment group, party B is on the opposite side of the spectrum but only 0.5 units away from the centre.Party A is always on the same side as the respondent and just as far from the respondent as party B. When the respondent's self-placement is too close to one end for this to be possible, party A is at the most extreme position on the same side as the respondent.In this study, we focus on questions about party B, but the effect of the presence of party A is tested, and the results are even stronger without it (SI5).
The design allows us to measure and prime normative considerations against supporting a candidate from the other side.To demonstrate that such considerations exist, we need to demonstrate that a liberal (for example) believes she should vote for a liberal candidate, not just because of the spatial distance between the individual and candidate but because they both come from the same (liberal) group.This requires us to control for the spatial part of an ideological identity.Past work on this problem assumes a proximity spatial function (voters prefer the party/candidate spatially closest to them) and interprets any deviation from this as the effect of a non-spatial component (Fiorina 1976; Jessee 2012).The limitation is that if a different spatial function applies, this misspecification will be interpreted as evidence of a non-spatial component.Ultimately, a vast number of spatial functions may apply, including those with more than one spatial dimension.
Our design eliminates the need to know the functional form or the dimensionality of an individual's spatial ideology.We allow for the possibility that different individuals use different spatial functions.Consider the difference in Figure 1 in what is seen by a respondent (r i ) depending on whether they are assigned to treatment or control.
Since we randomly assign subjects to treatment and control, we assume the average distance of respondents from party B is visually the same in the treatment and control groups, except that the centre line places party B in a different category for treatment group respondents but not for control group respondents. 8Different responses to party B by those in treatment and control are then attributable to the categorization of the party (left/liberal or right/conservative) and not spatial differences. 9 Q2 asks the respondent how much others with the same ideological identity would approve/ disapprove of them voting for a candidate from party B (on a 0 to 10 scale).This captures the normative considerations derived from their ideological group about voting for party B. Since spatial differences are controlled, the difference between treatment and control is a direct measure of the ideological group norm against voting for the other side.
Q3 then asks how likely the respondent would be to vote for a candidate from party B (on a 0 to 100 scale).Again, because spatial differences are controlled, the difference between treatment and control is a direct measure of the disutility of violating the group norm that one should not vote for a party on the other side and its effect on vote choice.

7
We exclude respondents that took less than five seconds to answer Q1 and less than ten seconds to answer Q2, on the basis that this is not long enough to read and understand the questions.

8
For evidence of balance across groups on several pre-treatment covariates and distance from the centre, see SI3.

9
A party on the other side might appear further because the centre acts as a heuristic for distance.This is consistent with the categorization theory if this is because the party is perceived to be in a different ideological category.The results we present about norms suggest that this is the case.
Hypothesis 1) There is a norm against voting for the other side.Controlling for spatial position, individuals expect others with the same ideological identity to approve more (disapprove less) of them voting for a candidate with the same ideological identity compared to a candidate with the opposite ideological identity.
Hypothesis 2) Violating norms is costly and affects vote choice.Controlling for spatial position, individuals are more likely to vote for a candidate with the same ideological identity compared to a candidate with the opposite ideological identity.

Results -Part 1
Figure 2 shows the average expected approval of voting for a candidate from party B on the opposite and same side of the ideological spectrum.Consistent with our hypothesis, expected approval is higher if party B is on the same side.For British respondents, the difference is 0.42 (p-value < 0.001) on a 0 to 10 scale. 10For American respondents, the difference is 0.48 (p-value < 0.001).The greater disapproval expected for voting for a candidate on the opposite side vs the same side, holding spatial distance constant, demonstrates that individuals perceive a norm against crossing the centre of the ideological spectrum. 11o demonstrate that individuals anticipate a cost for violating this norm, we explore the effect of norms on vote utility by comparing the average likelihood of voting for a candidate from party B when that party is on the same side of the spectrum as the respondent and when that party is on the opposite side, again controlling for spatial differences.Looking at Figure 3, we find that the likelihood of voting for a candidate from party B is higher when party B is on the same side.For British (American) respondents, the difference is 3.3 (5.6) on the 0 to 100 likelihood scale (p-values < 0.01).

Experimental Design -Part 2
Given the evidence that voting for the other side is seen as a norm violation and creates a disutility that alters vote likelihood, we now aim to assess whether increasing the salience of ideological group norms increases this disutility.We do this by demonstrating that when respondents express a personal preference that is incongruent with the norms of their ideological group, they experience an internal conflict, and this conflict is increased by making the norms of their group more salient.
We use responses to a fourth question (Q4), which asks individuals their positions on 12 issues from a shortened version of the Wilson and Patterson conservatism scale (1968) developed by Henningham (1996).This question was only put to the British sample.Previous work shows that right-/left-wing individuals express broad normative agreement on what position members of their group should take on the issues from the conservativism scale (Pickup, Kimbrough, and  de Rooij 2022).By comparing an individual's responses to the agreed-upon position as revealed in that study, we can identify incongruent responses: ones that violate group norms.We then use a response time test to determine if individuals experience a conflict when their responses violate group norms.
Prior evidence suggests that when reporting traits about the self that are incongruent with the normative expectations of the identity group, individuals take longer than when they are reporting traits that are congruent (Smith and Henry 1996).This is because the mental representation of the self and the group are linked as two dimensions of a single self-representation (Turner et al.  1987).Therefore, when an individual reports a trait incongruent with group norms, they experience a conflict.This conflict reflects the cost of violating group norms, and working through this conflict increases the time it takes to report that trait.Accordingly, we expect individuals with identity-incongruent preferences to take longer to report their positions than individuals without conflict.
Individuals who were asked about a candidate from a party on the opposite side of the spectrum (specifically Q2&Q3) were directly primed to think about the norm against voting for the other side.Those who were asked about a candidate on the same side of the spectrum still had ideology primed but did not have their group's norms explicitly primed.If the conflict an individual experiences when considering an incongruent personal preference is due to the cost of violating the norms of the identity, we would expect those primed to think about group norms to experience a stronger conflict and therefore take even longer to report incongruent positions.To identify evidence of a normative conflict, we regress the time it took respondents to respond to Q4 on the number of responses that were incongruent with group norms, interacted with whether the individual was primed to think of group norms: Hypothesis 3) Norm salience increases norm violation costs.When ideological group norms are made salient, individuals will take longer to report preferences that are incongruent with group norms.

Results -Part 2
For each additional incongruent item, response time increases by an average of 0.83 seconds (p-value = 0.052) for those not primed to think about group norms and 7.05 seconds (p-value < 0.001) for those who were. 13 The norm prime is experimentally randomized, while the number of incongruent items is an observational variable, so it is the difference between these two effects that gets at the causal effect of norm priming.The difference is both large and statistically significant (p-value < 0.001) providing evidence that primed individuals experience greater conflict due to the increased cost of violating a group norm.We should expect this effect of the prime to increase with an individual's perception of the strength of group norms when expressing incongruent preferences. 14We test this with a threeway interaction: Figure 4 presents the effects of incongruence on response time.The effect increases with the magnitude of the vote norm for those primed to think of group norms.There is no such effect amongst those who were not primed.Norm strength is an observational variable, so again it is the difference between these two effects that identifies the causal effect of norm priming (p-value < 0.001).

Discussion
The categorization theory of voting introduced by B&D predicts that crossing the centrepoint of an ideological spectrum introduces a discontinuity in voters' willingness to support a candidate.The strength of the vote norm (measured using Q2) is calculated for individuals at each point on the ideological spectrum.The norm is averaged over an interval of plus or minus 5 units on the ideological self-placement scale.(See SI4).
We argue that this discontinuity arises because voters with an ideological identity face a utility cost of violating their group's most basic norm: don't support the other side.We conduct a twopart experiment that provides a sharp test of the theory and of our proposed mechanism.We confirm that voters are averse to 'crossing the line' controlling for any spatial effects and that this aversion (at least in part) reflects group norms against supporting the other side.Our paper bolsters the important insights of B&D, highlighting a key mechanism of the categorization effect and using a controlled experiment to complement B&D's observational data.
Our findings have implications for another theory of vote choice: the Reputational Premium (RP) theory (Sniderman and Stiglitz 2012 (S&S)).This theory says that voters are particularly attracted to co-partisan candidates who take 'positions consistent with the policy outlook of their party' (p. 7).Set in the U.S. context, S&S propose the 'order rule' by which voters determine if a candidate is 'consistent': it is necessary and sufficient that the candidate is on the correct side of the other party's candidate.The order rule implies that a Republican voter gets an additional utility from supporting a Republican candidate so long as that candidate is to the right of the Democrat opponent.A Democrat voter gets an additional utility from supporting a Democrat candidate so long as that candidate is to the left of the Republican opponent.
At first glance, this looks similar to the categorization theory because both models assign a utility bonus to candidates that are on the 'correct side'; however, the models differ in whether they refer to the correct side of another candidate (RP theory) or to the correct side of the centre (categorization theory).They also differ in the mechanism by which this bonus occurs: a reputational premium in one case and norms in the other.
S&S give serious consideration to the hypothesis that the centre of the ideological spectrum matters.It is difficult to compare our empirics to theirs, given the different research designs (more on this in SI7) but S&S argue against this hypothesis on the grounds that there is no objective criterion for determining whether a candidate is on the right or left side of the policy space (S&S, p. 83).We accept that there is no objectively-defined centre or definition of liberal/conservative. 15 However, we disagree that informed voters (that is, programmatic partisans in S&S's language) are therefore unable (or unwilling) to label a candidate as liberal or conservative.
The categorization theory is about perceiving candidates/policies as falling within ideological categories, rather than objectively defining the categories, and the centre is simply the (perceived) boundary between categories.This can differ from voter to voter and across time and space; the voter need not even be able to articulate where the centre is in policy space.All that is required for the categorization theory to have implications for vote choice is that voters label candidates as liberal/left or conservative/right.To test whether voters can and will do this, we ran a survey 13-19 December 2022 (N = 1,000).Amongst 'programmatic partisans' (N = 473), 73 per cent identify their district's candidate for the U.S. House of Representatives in the previous midterm election (8 November 2022) as a 'liberal' or 'conservative'. 16his evidence demonstrates that many voters do place candidates into ideological categories, as the categorization theory requires.Coupled with our experimental evidence that the centre matters for vote choice, this has one of two implications for the relationship between the RP theory and categorization theory.The first possibility is that we might redefine where along the ideological spectrum a candidate can receive the RP.Our results suggest that being 'consistent with the policy outlook' might require being labeled as on the correct side of the ideological spectrum.I.e., this interpretation would suggest that the order rule is necessary but not sufficient to generate a utility premium because a candidate would need to be both on the correct side of the opposition and on the correct side of the spectrum.Alternatively, we might refine models of vote choice to include both an RP and a categorization effect, one of which is activated by being on the correct side of an opposing candidate and the other of which is activated by being on the correct side of the ideological spectrum.Further experiments may be necessary to resolve this.
Another implication of our findings is that those who identify as moderate conservatives and moderate liberals may be less moveable than their moderate views would suggest, contributing to polarization.If voting for a candidate is perceived as supporting 'the other side', moderates may be unwilling to do so even if the other party candidate's policy platform is closer to their ideal than the platform of the candidate on their own side. 17Practically, this suggests that those seeking to build coalitions for policy change should avoid allowing their policies to become associated with an ideological label.The categorization effect may thus explain the appeal of political rhetoric identifying initiatives as bi-partisan or non-partisan; since parties are associated with an ideological 'side', rhetoric that divorces a policy from a party affiliation allows that policy to avoid being 'tarnished' in the eyes of some voters by its association with 'the other side' of the ideological spectrum.
Supplementary material.The supplementary material for this article can be found at https://doi.org/10.1017/S0007123423000315.

Figure 1 .
Figure 1.Experimental design.Treatment and control conditions, with centreline shown to respondents (upper figure) and without centreline (lower figure)

Figure 2 .
Figure 2. Effect of treatment on approval by others of voting for a candidate from party B, means with 95% confidence intervals

Figure 4 .
Figure 4. Effect of incongruence by strength of vote norm (no norm prime and prime), maximum likelihood estimates from survival model with 95% confidence intervals