EXISTING THEORIES

Spatial theories of voting share the assumption that voters are rational and will choose the alternative that gives them the highest utility based on spatial considerations. They differ, however, in the utility functions that translate the positions of voters and parties into utility losses. The most straightforward model of vote choice, the ‘proximity model’, holds that individuals vote for parties with positions most similar to their own.Footnote ⁷ For a given political dimension, we calculate the Proximity Term for voter i and party j as the absolute distance between the position of the voter (V _i ) and the position of the party as perceived by the voter (P _ij ), that is, |V _i −P _ij |.Footnote ⁸ This term is expected to have a negative coefficient, as it captures distances that voters are expected to penalize. The utility curve implied by the model peaks where voters and parties are at the same position. This is shown in the left panel of Figure 1, which displays the utility for voters located at −2, and +1, on a dimension from −5 to +5, as a function of a party’s position along the same dimension.

Fig. 1

Voter utilities according to the proximity and directional models

Rabinowitz and Macdonald present a competing ‘directional model’, drawing on earlier work on issue perception and symbolic politics.Footnote ⁹ The authors argue that the assessment of political parties or candidates reflects two considerations. The first is ‘whether the individual and candidate are in agreement about the direction public policy should take’.Footnote ¹⁰ If individuals and parties prefer the same direction, this will contribute positively to party assessment; if they do not, the contribution will be negative. Secondly, the authors argue that the strength of the contribution to party assessment will be an interaction of the intensities with which the voter and party are emphasizing a given direction: the further they both are from the ‘neutral point’, the stronger the response. The neutral points represents the point at which no desired policy change is implied, and is commonly operationalized as the center of the scale.Footnote ¹¹

Following Rabinowitz and MacdonaldFootnote ¹² we thus calculate the Directional Term as V _i ×P _ij , where the notation is the same as above, and V _i and P _ij are centered on the middle of the scale. As shown in the right panel of Figure 1, for a voter at a given position, the directional utility of voting for a party is a linear function of the party’s position. If the voter is on a given side, the utility will increase linearly as the party moves toward that side, crossing 0 when the party crosses the center. The role of the voter position is to change the slope of the function: the further the voter moves from the center, the steeper the slope. The same holds for party positions, of course: they change the slope of the utilities as a function of voter positions.Footnote ¹³

Both in theoretical discussions and empirical studies, the intensity aspect of directional theory has overshadowed the directional aspect. The motivation behind most work in this area has been to solve the puzzle of the ‘empty center’: the question of why parties and candidates appear to be more extreme than voters.Footnote ¹⁴ This emphasis on the intensity part of the model has also motivated the accumulation of numerous mixed models of spatial voting. Perhaps most important among these is Grofman’s discounting model, which has been further elaborated in subsequent work.Footnote ¹⁵ The key idea is that parties are unable to fully implement their proposals, due to within-party dynamicsFootnote ¹⁶ or systemic constraints in multiparty systems with coalition governments.Footnote ¹⁷ Thus voters are led to prefer parties more extreme than themselves in order to get the amount of policy change they would like. These models are all based on a proximity calculus, adjusted to accommodate the discrepancy between parties’ programs and actual policies.Footnote ¹⁸ We leave these additional models aside here, as they do not capture the effects we hypothesize to any greater extent than the two main theories that we focus on.

In addition to the development of mixed models, a vast literature has emerged that attempts to assess the relative merits of the proximity and directional theories.Footnote ¹⁹ Lewis and King argue, however, that arguments about which theory fits best tend to be based on assumptions that are hard or impossible to test.Footnote ²⁰ Recently, several experiments have brought the debate forward, concluding overwhelmingly in favor of proximity theory.Footnote ²¹ Overall, there is little doubt that proximity theory has considerable predictive power in voting behavior. We argue, however, that the existing theories of spatial voting, including proximity theory, overlook an important pattern that reflects categorization effects.

CATEGORIZATION THEORY

Research in cognitive science has repeatedly demonstrated that humans use coarse perceptual schemas that simplify information processing.Footnote ²² Under conditions of uncertainty, the categorization of objects permits the use of simple heuristics to make predictions regarding unknown object features.Footnote ²³ Work in judgement theory in social psychology has further shown that merely placing objects in categories influences individuals’ perceptions and evaluations of these objects.Footnote ²⁴ This form of bias is known as accentuation and involves a tendency for individuals to underestimate the differences between observations falling into the same category and to overestimate the differences between those falling into different categories.Footnote ²⁵ Furthermore, social identification theory holds that such effects are involved in the formation of social identities, as individuals not only categorize objects, but also people, including themselves.Footnote ²⁶ Because individuals partly derive their identities from self-perceived group memberships, they tend to attach strong feelings to such memberships, which in turn leads them to focus on, and exaggerate, the differences between group members and outsiders.Footnote ²⁷ In other words, identity formation is based on self-categorizations, which in turn leads to in-group favoritism.Footnote ²⁸

We argue that these findings are relevant to spatial voting, because voters operate with basic mental categories representing the sides of the political center. In particular, this applies to the most important political dimension in a given political system, yielding two encompassing categories. In most countries, it is common to speak of voters and parties as being either left-wing or right-wing, and these labels provide shortcuts to richer descriptions of the actors’ traits.Footnote ²⁹ As with other stimuli, the categorization of political actors according to their side of the ideological center is likely to involve the use of prototypes.Footnote ³⁰ A prototype left-wing actor may, for example, emphasize social and economic equality and express a willingness to use public policy to promote these values, while a right-wing actor may emphasize individual responsibility and freedom from government intervention. Thus categorization is also accompanied by issue packaging, permitting the use of coarse party preferences as a heuristic. Even if specific issue dimensions might allow refined distinctions between parties, they are eventually embedded within a coarse, category-based assessment framework. Theories of party branding exemplify this logic, suggesting that voters perceive parties’ positions along salient dimensions as signals of what they generally stand for.Footnote ³¹

Drawing on these arguments, we expect voters to assess and be conscious of their own side of the ideological center. As ideological positions tend to be highly consistent over time,Footnote ³² we further assume that these self-categorizations matter for voters’ identities, expressing some of their most fundamental values and attitudes. As a consequence, we expect voters to assess whether a given party falls in the same category as themselves – in other words, whether the party is on their side, being one they broadly agree with and potentially could vote for. The first empirical implication of our theory is therefore that parties receive a more favorable assessment when they are on the same side as the voter in question. Furthermore, allowing for the existence of a neutral center category, we expect voters to penalize parties on the opposite side more than those in the center. As illustrated in the next section, these effects are not captured by the dominant theories of spatial voting.

In a setting with many parties, however, a pure categorization model is unlikely to be adequate on its own, as voters may still have to choose among several parties on their side. Existing research suggests that individuals facing a large number of options are indeed likely to first choose a broad category and then make a more specific choice within this category.Footnote ³³ In the present context, such a within-category choice could be based on one of several available decisions rules. Voters could make a random draw, choose based on non-ideological factors (for example, experience, charisma or competence), or conduct a more finely grained assessment among parties on their side, applying additional functions of party and voter positions. This last scenario is particularly interesting because it implies that different spatial rules may interact with categorization effects. While voters need to pick a favorite to win their vote, it matters less how they rank their least-favored parties. Thus according to our theory, the predictive power of existing spatial rules should increase when categorization is insufficient to distinguish among the alternatives – that is, for parties located on the same side as the voter in question. If, for example, voters use a proximity rule, we expect that its impact on vote choice increases when parties and voters are on the same side.

Furthermore, the argument that voters think in terms of categories has implications for the issue of reverse causation from preferences to party perceptions. A common challenge to analyses of proximity voting relates to a phenomenon known as projection or rationalization bias, which refers to the tendency for voters to exaggerate their ideological agreement with their preferred political parties.Footnote ³⁴ Given the utility maximization principle of spatial models, this endogenous process complicates the identification of ideological voting. In the current setting, however, the issue of reverse causation also offers an additional opportunity to test our theory, which seeks to describe the lenses through which voters understand politics. While it is possible that some voters bring parties they like over to their side to justify their preferences, this would only confirm that voters do think in terms of these broad categories. In fact, if our theory is correct, we should observe categorization patterns of projection bias. We test this implication in the analyses below, and – as a follow-up in the robustness section – we also implement our analyses using objective party placements in order to ensure that our results are not entirely driven by projection.Footnote ³⁵

SPECIFICATION

If voters do indeed consider whether parties are on their side or not, then some steps along the ideological scale will be more significant than others. In particular, we expect party preferences, as functions of party and voter placements, to exhibit discontinuities at the center of the scale. The expected effects of being on the same and opposite sides are most easily illustrated keeping either voter or party positions fixed. Figure 2a thus illustrates the expected pattern for voters who place themselves left of center.

Fig. 2

(a) Pure categorization model (b) categorization effects conditioning proximity and directional effects

Assuming the existence of a neutral category, we allow the effect of being on opposite sides to be different from that of being on the same side. In our parametric analyses, we therefore employ two dummy variables to capture the states of relevance. Indicator S captures Same Side status: S={1 if V _i ×P _ij >0; 0 if V _i ×P _ij ≤0}, while indicator O captures Opposite Side status: O={1 if V _i ×P _ij <0; 0 if V _i ×P _ij ≥0}, where the voter and party positions (V _i and P _ij ) are centered on the geometric middle of the scales. Implementing the categorization model as a regression equation, we get:

(1) $$Y_{{ij}} =\beta _{0} {\plus}\beta _{1} S_{{ij}} {\plus}\beta _{2} O_{{ij}} {\plus}{\varepsilon}_{{ij}} ,$$

where β ₀ denotes the average preference in the neutral category, β ₁ and β ₂ are the effects of same and opposite side status, and ε _ij is an error term.

As mentioned, where multiple parties are on the same side as the voter, categorization is not sufficient to distinguish between the alternatives. Voters may thus employ additional spatial rules to select among these parties. Following this logic, we expect alternative utility functions to be more important in distinguishing among parties on the same side as the voters. To incorporate this expectation into our model, Equation 1 needs to be augmented by the inclusion of appropriate interaction terms, allowing the impact of other functions to depend on categorization:

(2) $$Y_{{ij}} =\beta _{0} {\plus}\beta _{1} S_{{ij}} {\plus}\beta _{2} O_{{ij}} {\plus}f(V_{i} ,P_{{ij}} ){\plus}\beta _{3} S_{{ij}} \,f(V_{i} ,P_{{ij}} ){\plus}\beta _{4} O_{{ij}} \,f(V_{i} ,P_{{ij}} ){\plus}{\varepsilon}_{{ij}} ,$$

where f(V _i , P _ij ) is an unspecified function providing further distinctions. If voters were to apply a proximity logic based on absolute distances, we would get a pattern like that in the left panel of Figure 2b, while a directional logic would yield a pattern like that in the right panel. For now, we remain agnostic about which other functions voters may apply, but we expect the effect of such functions to be stronger when voters and parties are on the same side.

The empirical analysis is divided into five sections. First, we present a set of illustrative plots, making no assumptions about f(V _i , P _ij ). We thus explore the presence of categorization effects examining specific scenarios of party and individual ideological placements without imposing a specific spatial utility function. These results clearly favor a model combining categorization and proximity effects. Our next step includes a more tailored analysis to test the presence of categorization effects when proximity is held constant, while directional theory predicts a different outcome. Next, we test Equation 2 in order to investigate the mentioned corollary of categorization effects, namely that other spatial criteria will weigh more within the subspace characterized by voter-party convergence. Then, we address the presence of categorization in projection bias, before the last section reports a set of robustness checks.

DATA AND OPERATIONALIZATION

To test the role of categorization as a general feature of spatial voting, we use data from the European Election Study (EES),Footnote ³⁶ which covers a wide range of countries. We focus on the dominant ideological dimension in these countries, which is the left-right continuum. The EES includes eleven-point measures of left-right positions (scales from 0 to 10) for both voters and parties.Footnote ³⁷ To ensure homogeneity in the meaning attached to this scale, we concentrate on established democracies.Footnote ³⁸ We thus base our analysis on fifteen EU countries: Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, Sweden and the United Kingdom.

We measure the strength of preferences by using the respondents’ ratings of the parties, expressed as their likelihood of ever voting for them. This ‘propensity to vote’ question (PTV) facilitates cross-national comparison and is often used to capture voters’ party preferences.Footnote ³⁹ Our unit of analysis is neither voters nor parties, but rather combinations of the two. We thus transform our dataset into one consisting of party × individual observations.

We expect voters to use category 5 on the eleven-point scales as a neutral category defining two broader categories on each side. To ease the construction and interpretation of the relevant terms, we center the scales on 5, giving them a minimum of −5 and a maximum of +5. It is important to note, however, that the survey questions and answer categories do not in any way involve a neutral point, middle or sides defined by a threshold. They are presented as continuous scales that would seem more fit for employing a pure proximity logic. Thus if voters are found to understand such a scale in terms of broader categories without being asked to do so, this will be valuable evidence against a pure proximity logic.

VISUAL INSPECTION

Choosing to be agnostic about the possible additional utility functions voters apply, we begin with a visual exploration, avoiding parametric restrictions. Our plots are based on local sample means, conditional on party and voter placements. As discussed above, keeping voter positions fixed, the status of being on the same or opposite sides becomes a deterministic function of party positions, and vice versa. As explained, we would expect discontinuities on each side of the center. Furthermore, we would expect other spatial rules to have more pronounced effects when parties and voters are on the same side.

Figure 3 shows average party preferences over different voter positions for each relevant party placement on the left-right scale. For example, the upper left graph of the figure presents the average preference score for a party located at point −1 (left of center) over the whole range of voter positions along the left-right axis, while the lower-left graph shows the same for a party at +1 (right of center). As the figure shows, for almost all party placements there are clear discontinuities as we move from one side of the center to the other, and as explained above, these would not be expected based on a pure directional or proximity model. However, the discontinuities do come in addition to a pattern of finer distinctions, which clearly resemble a proximity model with absolute distances. Furthermore, this pattern is stronger when parties and voters are on the same side: the plots are consistent with the hypothesis that these finer distinctions are conditional on categorization.

Fig. 3

Average party preferences over left-right self-placement holding party placement constant Note: the gray bin represents the party placement (measured by respondents’ subjective placements). The solid line denotes the average PTV score and the dashed lines show 95 per cent CIs. The graphs are arrayed by starting with the most centrist positions and moving toward the most extreme positions. The upper series includes left-of-center parties and the lower panel includes right-of-center parties.

Figure 4 shows the same as Figure 3, but keeping voters (rather than parties) fixed. Again, we see categorization effects, albeit somewhat weaker than in the previous plot. Furthermore, the conditioning effect of categorization can also be seen here. When it comes to parties on the opposite side, voters are more indifferent and their preference scores are less contingent on the smallest distance criterion. These initial analyses thus offer preliminary evidence of categorization effects. The next sections extend this evidence by engaging in a more systematic testing of the constituent parts of the theory.

Fig. 4

Average party preferences over left-right party placement holding self-placement constant Note: the gray bin represents voters’ position. Party positions are measured by respondents’ subjective placements. The solid line denotes the average PTV score and the dashed lines show 95 per cent CIs. The graphs are arrayed by starting with the most centrist positions and moving toward the most extreme positions. The upper series includes left-of-center voters and the lower panel includes right-of-center voters.

CRITICAL CASES

To strengthen the inference that categorization matters, we also conduct more formalized tests, carefully selecting the observations to be compared. In order to distinguish our model from the directional and proximity models, we focus on so-called critical cases,Footnote ⁴⁰ in which the three models produce clearly diverging predictions. We conduct four tests, each involving a pair-wise comparison of two scenarios. We thus have eight scenarios, each involving one voter position and two party positions.

As illustrated in Figure 5, the ‘treatment’ scenario of the first comparison (1 _T ) involves a voter (V) at −1, a party (P _A ) at −3, and another party (P _B ) at 1.Footnote ⁴¹ The parties are at an equal distance from the voter, so the proximity model does not predict that the voter will prefer one party over the other. According to directional theory, however, V should prefer P _A : the directional scores are 3 and −1 for Party A and B, so the difference between them is 4 (in A’s favor). The respective ‘control’ scenario (1 _C ) is generated by moving all positions two steps to the left on the scale. According to proximity theory, the voter should still be indifferent. According to directional theory, however, things are now much more clear-cut: the directional values are 15 and 3 for Parties A and B, respectively. While the difference in directional scores for P _A and P _B was 4 in 1 _T , it is 12 in 1 _C . If directional theory is correct, we should expect V to prefer P _A to P _B to a higher degree in the second than in the first scenario.

Fig. 5

Four comparisons of scenarios with and without categorization Note: the voter position is denoted V, while the positions of Parties A and B are denoted P _A and P _B . The comparisons are numbered 1 to 4, and consist of a ‘Treatment’ Scenario (where categorization implies a penalty for P _B compared to P _A ) and a ‘Control’ Scenario (where both parties are on the same side), subscripted T and C, respectively.

Our categorization model produces a different prediction. In scenario 1 _T , Party A is on the same side as the voter, while Party B is on the opposite side. In scenario 1 _C , both parties are on the same side as the voter. Hence, V should prefer P _A over P _B to a greater extent in scenario 1 _T than in 1 _C . As Figure 5 shows, we also investigate scenarios that replicate the ones just presented, but on the right side of the scale (comparison 2). In comparisons 3 and 4, we test the role of categorization while letting the proximity of the two parties vary. In each of the scenarios involved, the proximity model predicts that Voter V will prefer Party B over A, while directional theory predicts A over B. However, the distances are kept constant from one scenario to the next, so proximity theory still predicts no difference between the two scenarios. The directional model yields the same prediction as before – a negative difference-in-differences. According to the categorization model, there should be a positive difference-in-differences. However, these tests are more challenging for the categorization argument because the distinction is not between same versus opposite side but rather between same-side versus neutral status.

For each scenario, we select voters who place themselves at point V and have located at least one party at P _A and at least one party at P _B . We create a binary indicator identifying the alternative favored by the directional model (always Party A). We then pool the observations for the two scenarios to be compared, create another binary indicator identifying the ‘treatment’ scenarios and interact this with the indicator identifying Party A. The resulting coefficient denotes the difference in the average difference between the preference scores for Parties A and B, going from scenario C to T. A negative coefficient would be consistent with directional theory, while a positive coefficient would be consistent with categorization theory. To account for the clustering of preferences within individuals, we include individual fixed effects, and use robust standard errors clustered at the individual level.

Figure 6 shows the results, plotting the coefficients of interest along with 95 per cent confidence intervals. As can be seen, the point estimates are all positive; two are clearly significant, while one is barely significant, and one is barely insignificant. As explained above, these estimates are in line with the categorization model, and contradict directional theory.

Fig. 6

Estimated differences in differences for comparisons 1 to 4 Note: the dots represent the difference in the average differences between the preference scores for Party A and Party B, going from Scenario C to T. The error bars indicate 95 per cent confidence intervals. The estimations include individual fixed effects and the standard errors are clustered at the individual level.

GENERAL ANALYSIS

To obtain more general estimates of the effects, we now turn to a more standard regression framework. Table 1 reports a set of regression models, implementing the categorization model along with other spatial functions. Model 1 includes the Proximity Term, the Directional Term, and indicators of Same Side and Opposite Side status. The estimated effect of Same Side is close to 1 on the eleven-point preference scale, while that of Opposite Side is about −0.3, and both estimates are highly significant. The effect of proximity is also highly significant and has the expected sign. The estimate for the Directional Term appears to be statistically significant, but it has the wrong sign, suggesting this model is misspecified. This conclusion is also corroborated by the plots shown above, which indicate no trace of a directional effect. The Directional Term is therefore dropped in Model 2, without a notable loss in explanatory power or change in the other estimates. The categorization effects are still significant and have considerable magnitude.

Table 1

Models of Spatial Voting with Categorization Effects

Note: the dependent variable is the propensity to vote for a party (see the Data section for details). Party positions are measured by respondents’ subjective placements. The cell entries are ordinary least squares (OLS) regression estimates, with robust standard errors, clustered at the individual level, in parentheses. *p<0.05, **p<0.01, ***p<0.01.

There is one reason for concern about the reported results, however. Using the whole set of observations and a linear implementation of the Proximity Term, the analyses involve some extrapolation. All three side-statuses can only be observed for proximity values of 2, 3 and 4. (It takes two steps to move from the same to the opposite side, while with a distance of 5 or larger it is not possible to be on the same side. With a proximity value of 1, it is only possible to compare either same or opposite side status to the neutral status.) In other words, there is only common support for the mentioned proximity values. Model 3 in Table 1 reports an analysis only including observations where the Proximity Term is 1, 2, 3 or 4. It further includes proximity-fixed effects, ensuring that proximity effects are fully controlled for. The resulting categorization estimates are only slightly weaker than before, with a Same Side estimate of about 0.8 and Opposite Side estimate of about −0.3.

As discussed above, voters need more criteria than side categorizations to distinguish between several parties on a given side, and we expect these criteria to play a larger role for parties on the same side as voters, as the voters need to pick a winner of their vote. So far, our analyses show that when categorization in terms of sides does not suffice, voters apply a proximity logic to make finer distinctions. In Model 4, we therefore include an interaction between the Proximity Term and the categorization indicators. The results are in line with our expectations: the effect of the Proximity Term is almost twice as strong for parties on the same side as voters, compared to parties on the opposite side (−0.73 versus −0.40). Thus, categorization not only creates discontinuities in what proximity theory suggests is a continuous space, it also qualifies the impact of proximity considerations.

CATEGORIZATION EFFECTS IN PROJECTION BIAS

We now turn to another implication of our theory. Rationalization or projection bias presents a considerable challenge for the proximity model, as it is built on the assumption that perceptions precede utilities. A key point for us is that if our theory is correct, projection should reflect the coarse categories examined above. A classic idealized model of projection considers the interaction between individuals’ self-placements and their party evaluations. The more a voter likes a party, the more likely she is to perceive this party as being closer to her own position than it really is. As this process has been suggested as an alternative explanation of proximity patterns in voter preferences, it has invariably been assumed to operate in a linear fashion throughout the ideological scale. In contrast to this widespread assumption, the theory presented here implies categorization effects: the incentive to misplace a preferred party’s true position is significantly strengthened when this means bringing it to one’s own side. Thus, considering two individuals with the same distance to their preferred party, projection should be more evident for the individual who would otherwise find the party at the opposite side of the center.

To test this hypothesis, we draw on (but also significantly modify) existing models of projection bias.Footnote ⁴² We present two different models, both of which use parties’ sample mean placements as a measure of their ‘true’ positions.Footnote ⁴³ In our first model, the dependent variable, W _ij , is constructed as a binary indicator of ‘mis-categorization’, that is, party-individual combinations where the respondent placed the party at the opposite side of the sample average. Our measure of party utility, which is the same as before, is now employed as an independent variable, denoted Y _ij . In our simplest model, this variable is interacted with two binary indicators of same and opposite sides, $$S_{{ij}}^{M} $$ and $$O_{{ij}}^{M} $$ , where mean party placements are used to locate the parties. The first indicator thus identifies observations where respondents are on the opposite side of the mean party placement, whereas the second identifies those where respondents are on the same side as the mean party placement. The interaction between party evaluations and these two dummies reveals the impact of categorization-based projection: the more a voter likes a party on the opposite side, the more likely she is to misplace the party so as to find it on her own side. Our simplest model is thus:

(3) $$W_{{ij}} =\beta _{0} {\plus}\beta _{1} O_{{ij}}^{M} {\plus}\beta _{2} S_{{ij}}^{M} {\plus}\beta _{3} Y_{{ij}} {\plus}\beta _{4} O_{{ij}}^{M} Y_{{ij}} {\plus}\beta _{5} S_{{ij}}^{M} Y_{{ij}} {\plus}{\varepsilon}_{{ij}} .$$

In this model, categorization effects in projection are mainly captured by β ₄ and β ₅, although these coefficients should be combined with the main effects of preference strength (β ₅) and side status (either β ₁ or β ₂) to obtain the complete marginal effects of preference strength, conditional on side status. We go one step further, however, and allow for non-linearity by using penalized smoothing splines in a generalized additive model (GAM). We estimate three smooth terms to capture the effect of preference strength, conditional on whether voters are on the same side as the mean party placement $$( {S_{{ij}}^{M} =1} \right)$$ , opposite side $$( {O_{{ij}}^{M} =1} \right)$$ or neither $$( {S_{{ij}}^{M} =O_{{ij}}^{M} =0} \right)$$ .

Our second model aims more directly to capture the underlying idea behind projection models, namely that voters might over- or under-estimate their ideological distance to parties according to their non-ideology-based preferences. Thus the dependent variable is now a measure of divergence between the perceived and ‘objective’ distances between parties and voters: $$\mid \!P_{{ij}}^{P} {\minus}V_{i} \!\mid\!{\minus}\!\mid\!P_{j}^{M} {\minus}V_{i} \!\mid$$ , where $$P_{j}^{M} $$ denotes the mean left-right position of party j, $$P_{{ij}}^{P} $$ denotes the position of party j as perceived by voter i, and V _i denotes voter placements. We model this difference as a function of party utility (Y _ij ), the two indicators of same and opposite side $$( {S_{{ij}}^{M} \,{\rm and}\,O_{{ij}}^{M} } \right)$$ , and the interaction between these and party utility. We expect that the need for rationalization will be stronger when preferred parties’ ‘true’ positions are on the opposite side of voters. Following the standard convention for first-differenced models, we also include the perceived ideological distance between parties and voters $$( {\mid\! P_{{j}}^{M} {\minus}V_{i} \!\mid} \right)$$ as a predictor in some of the models (reported in full in the Appendix). The resulting model is thus:

(4) $$\mid \!P_{{ij}}^{P} {\minus}V_{i} \!\mid\!{\minus}\!\mid\!P_{j}^{M} {\minus}V_{i} \!\mid\,=\beta _{0} {\plus}\beta _{1} O_{{ij}}^{M} {\plus}\beta _{2} S_{{ij}}^{M} {\plus}\beta _{3} Y_{{ij}} {\plus}\beta _{4} O_{{ij}}^{M} Y_{{ij}} {\plus}\beta _{6} \!\mid\!P_{{j}}^{M} {\minus}V_{i} \!\mid\!{\plus}{\varepsilon}_{{ij}} .$$

We expect that the stronger the preference for the party, the greater the underestimation of the distance between party and voter. Such evidence of projection, however, should be mediated by whether the party is already on the same side as the voter. If a preferred party were on the opposite side of the voter, this would make the need for projection stronger and thus increase the tendency to underestimate ideological distance. Testing this expectation, we again use a generalized additive model to allow a more flexible estimation of the role of party utility for projection.

Figure 7 reports the results from both models. The first panel presents the key estimates for the first model and demonstrates considerable categorization effects in projection bias. The graph shows that when a voter strongly dislikes a party on her side (Y _ij =0), the probability of miscategorizing the party (moving it to the opposite side) increases. This kind of misplacement becomes less likely as the evaluation of the party grows more favorable. Similarly, a voter who strongly likes a party on the opposite side is much more likely to move this party to her own side. In contrast, if she dislikes a party on the opposite side, the probability of making such a miscategorization decreases considerably.Footnote ⁴⁴ The second panel shows that as party utility increases, the ideological distance to the party is increasingly underestimated. However, this effect is stronger for parties located on the opposite side than for parties on the same side as voters. The slope of Y _ij is steeper for parties on the opposite side. Taken together, these results strongly support the notion that voters categorize parties as well as themselves in terms of their side of the center, and that they find these categories significant.

Fig. 7

Categorization effects in projection bias Note: the left panel shows the effects of party preference strength on the probability of placing a party on the ‘wrong side’ compared to its sample mean placement, conditional on the mean party placement being on the same or opposite side of the voter. The right panel shows the effects of party preference strength on the subjective overestimation of the distance to a party, conditional on the mean party placement being on the same or opposite side of the voter. As shown in the Appendix, using expert surveys to measure party positions yields similar results. The plots are based on GAMs with penalized smoothing splines. The dashed lines report 95 per cent confidence intervals.

ROBUSTNESS

Lastly, it worth assessing the robustness of our results. First, as many readers may be unfamiliar with our measure of party preferences, the PTV, and some may consider actual vote choice a more important and relevant outcome, we also implement our model analyzing vote choice. In Appendix Table A9, we report a full replication of Table 1 with vote choice as the dependent variable, and the results are substantively identical to those we report above.

Another issue arises from the projection effects shown in the previous section: the question of whether the patterns we find are mainly driven by subjective perceptions (and misperceptions) of positions along the ideological scale, or whether they are still present when more objective measures are used. We address this using the left-right party positions provided by the 2010 Chapel Hill Expert Survey.Footnote ⁴⁵ We implement our analyses for both PTVs and vote choice, and the results are reported in Table 2.Footnote ⁴⁶ The results are substantively very similar to those reported earlier, which implies that the categorization effects are informed to a considerable degree by objective party placements rather than being driven by individual misperceptions.

Table 2

Results with Party Positions Based on Chapel Hill Expert Surveys

Note: the cell entries are OLS regression estimates, with robust standard errors, clustered at the individual level, in parentheses. *p<0.05, **p<0.01, ***p<0.01.

Another potential concern is that our findings are confounded by partisan attachments. It is indeed likely that subjective perceptions of ideological proximity to some extent may be overestimated for parties with which voters strongly identify. However, the robustness checks above – using objective party placements – already guard against this possibly confounding effect, and show that our results hold in the absence of perception biases. Furthermore, it is also very likely that party identification is partly driven by ideological proximity, which is why we generally do not include party identification in our models, as this would generate post-treatment bias. Nevertheless, as another robustness check, we replicate the analyses of Table 1, adding a measure of partisanship that captures both the direction and the intensity of partisan attachments. Further information is provided in Appendix Table A10, which also presents the results. All key findings are robust to the inclusion of party identification, suggesting that ideological categorizations constitute an independent and more general source of identification, and generate effects beyond those that can be accounted for on partisan grounds.

A final question is whether categorization also applies to the American context. In this case, we would not focus on the left-right dimension, but on the conceptually similar liberal-conservative dimension. More importantly, the country’s two-party system could render the ideological categorization of political actors superfluous, as party-based divisions could represent an equivalent and equally encompassing form of categorization. To address the question of whether ideological categorization is relevant in the United States, adding predictive power beyond party identification, we conduct an analysis of vote choice using the American National Election Studies (ANES) and report the results in Appendix Table A11.Footnote ⁴⁷ We use all surveys since 1972, because since then respondents have been asked to place themselves and parties on a 1–7 liberal-conservative scale. We first replicate Table 1, showing that categorization effects are also present in the American context. We then add party identification as a control variable (despite the risk of post-treatment bias), and show that the categorization model has explanatory power beyond that of party identification.Footnote ⁴⁸