2.1 Formalizing Constraint and Multidimensionality

We now formalize constraint and multidimensionality in the context of canonical ideal point models. This will result in some observable implications that we can use to empirically identify the level of constraint and dimensionality in a population given a sample of its political choices.

We couch our discussion in terms of the familiar quadratic-utility spatial voting model used in Clinton, Jackman, and Rivers (2004, hereafter CJR).Footnote ³ Specifically, we will suppose the political actors we are studying—whether they be members of Congress, survey respondents, and so on—have an ideal point $\gamma _{i}$ located in some common D-dimensional Euclidean space. When considering a choice between two policy proposals, a “yea” policy located at point $\zeta _{j}$ and a “nay” policy located at $\psi _{j}$ , voters’ utility is a function of the distance between their ideal point $\gamma _{i}$ and the policy positions, plus a mean-zero idiosyncratic preference shock independently distributed across actors and proposals. Under the assumption of normally distributed shocks, it is simple to obtain an expression for the probability actor i chooses the yea option on choice j, denoted $y_{ij}=1$ . Averaging over preference shocks, it is given by

(1) $$ \begin{align} P(y_{ij} = 1 \mid \alpha_{j}, \beta_{j}, \gamma_{i}) &= \Phi(\alpha_{j} + \beta_{j} {{}}^{\mkern-1.5mu\mathsf{T}} \gamma_{i}), \end{align} $$

where $\alpha _{j}$ and $\beta _{j}$ are functions of the policy locations and the distribution of shocks.Footnote ⁴

We use this model to characterize the distinction between multidimensionality and constraint. Implicit in the model is the dimensionality of the common policy space. The parameters $\gamma _{i}$ and $\beta _{j}$ lie in some D-dimensional Euclidean space $\mathbb {R}^{D}$ representing the space of possible policies. For instance, Treier and Hillygus (Reference Treier and Hillygus2009) consider a two-dimensional policy space to reflect economic and social issues. We might label the positive end of this space in both directions to refer to “conservative” policies, so an actor with $\gamma _{i} = (-1.5, 3.2)$ would prefer “liberal” economic policies and “conservative” social policies.

To further unpack this, focus on the linear predictor of actor i and choice j:

(2) $$ \begin{align} \alpha_{j} + \beta_{j} {{}}^{\mkern-1.5mu\mathsf{T}} \gamma_{i} &= \alpha_{j} + \sum_{d=1}^{D} \beta_{jd}\gamma_{id}. \end{align} $$

Equation (2) suggests that choice j is analogous to a (generalized) linear regression. The “intercept” $\alpha _{j}$ and “coefficients” $\beta _{j}$ change from choice to choice depending on the alternatives on offer, but the “covariates” $\gamma _{i}$ stay the same for actor i across choices. For instance, the mapping from economic and moral preferences to a tax policy question will differ from how those same preferences map onto an immigration policy question (different intercepts and slopes), but the underlying economic and moral preferences (covariates) stay the same.

Thus, we can think of the dimensionality D as the number of underlying preferences needed to explain expected utilities. When D is small, there are only a few key attributes that meaningfully distinguish between policies in expectation—all of the other variables that determine utilities are too idiosyncratic to be organized into a common policy space. However, when D is large, there is a greater variety of systematic political conflict. The residual incentives for voting yea or nay are still idiosyncratic, but the systematic components of utility involve trade-offs between a higher number of issue dimensions. With high dimensionality, actors might be balancing preferences along, say, tax policy, morality policy, immigration policy, foreign policy, etc., provided these preferences are sufficiently uncorrelated.Footnote ⁵

If multidimensionality is the correct number of covariates needed to model expected choice in Equation (2), then constraint is the amount of variation those covariates can explain. As we alluded to previously, constraint captures the idea that knowing an actor’s ideal policy, $\gamma _{i}$ , improves our ability to predict their choices. In the linear regression analogy, constraint is similar to the $R^{2}$ statistic: how much better we do in prediction after conditioning on the covariates $\gamma _{i}$ .

To see precisely how knowledge of $\gamma _{i}$ might improve our ability to predict choices, recall that the probability of a yea vote conditional on $\gamma _{i}$ is given by Equation (1), $P(y_{ij} = 1 \mid \alpha _{j}, \beta _{j}, \gamma _{i}) = \Phi (\alpha _{j} + \beta _{j} {{}}^{\mkern -1.5mu\mathsf {T}} \gamma _{i})$ . How does the probability of a yea vote change if we do not have knowledge of the ideal point $\gamma _{i}$ ? To compute this, we must imagine drawing an actor at random, which means we must draw a value of their ideal point from the population distribution. For illustration, suppose we draw the ideal points from a standard multivariate normal: $\gamma _{i} \sim N(0, I_{D})$ . Then, the population average probability of a yea vote on choice j is given by

(3) $$ \begin{align} P(y_{ij} = 1 \mid \alpha_{j}, \beta_{j}) &= \Phi\left(\frac{\alpha_{j}}{\sqrt{1 + ||\beta_{j}||^{2}}} \right), \end{align} $$

for all actors i. This is essentially an intercept-only probit model $\Phi (\delta _{j})$ with intercept $\delta _{j} = \alpha _{j} / \sqrt {1 + ||\beta _{j}||^{2}}$ that varies for each item j.Footnote ⁶

Equation (3) is the appropriate null model for understanding to what extent ideal policy preferences explain choices. When Equations (1) and (3) are different, then knowledge of an actor’s ideal policy helps explain their choices. Before knowing someone’s ideal policy, the prediction for their choice should be the same for everyone, Equation (3). If choices are unconstrained, then idiosyncratic components determine choices completely and thus ideal points $\gamma _{i}$ would be uninformative. In that case, there would be no difference between predictions made with ideal points and predictions made without them. However, once we know an actor’s ideal policy, and there is a high degree of constraint, our prediction for their choice should alter dramatically as we go from $P(y_{ij} = 1 \mid \alpha _{j}, \beta _{j})$ to $P(y_{ij} = 1 \mid \alpha _{j}, \beta _{j}, \gamma _{i})$ .

This discussion of constraint was specific to the individual actor i. To get a population measure of constraint, we can average over the population how much our predictions improve. This gives us the expected predictive power of ideal points relative to the null model.

To summarize our discussion, multidimensionality is a property of the agenda and how preferences are organized among the population as a whole. It is analogous to the (correct) number of covariates in a linear regression model. In contrast, constraint is how much individuals use these organized preferences to select the choices on offer. If the organized preferences matter, and we know actors’ ideal policies, we will make much different predictions than we would without that structure. Consequently, under high constraint, ideal points explain a large amount of variation in choices, while under low constraint ideal points are only mildly predictive of choices. Critically, multidimensionality and constraint are not mutually exclusive: any population/agenda combination can have high or low dimensionality and high or low constraint. There are no (logical) trade-offs between constraint and multidimensionality, and whether voters are multidimensional has nothing to do with whether they are constrained.

2.2 Empirical Implications

Having clarified the distinction between multidimensionality and constraint, we turn toward measuring these concepts in common data on political choices, such as surveys and roll-call votes.

First, we treated the dimensionality D as a fixed number in our theoretical discussion. Indeed, when fitting the ideal point model laid out above, we must make a choice about the dimensionality of the model we wish to fit. However, we do not know the true dimensionality D a priori, so it makes sense to think about D as a parameter we can infer. Measuring the dimensionality is, therefore, tantamount to learning the value of $D \in \{1,2,\dots \}$ that leads to the best approximation of the true data-generating process.

After learning the best-fitting dimensionality, we can assess the level of constraint by comparing the fraction of choices predicted by our fitted model to the fraction of choices predicted by the fitted null model that does not include ideal points. In a highly constrained population, nearly all of the variation that cannot be explained by the null model will be explained by the best-fitting ideal point model. However, in an unconstrained population, the best-fitting ideal point model will explain only slightly more variation than the null model. This perspective highlights that constraint is not binary, but is a matter of degree. Idiosyncratic preferences surely exist; the question is how important those preferences are in comparison to the systematic components determining political choices. In the next section, we describe our method for estimating this degree of constraint in any particular population–agenda combination.

3.1 Arguments for Out-of-Sample Validation

First, out-of-sample prediction is more directly aligned with the original definitions of constraint. For instance, Converse (Reference Converse and Apter1964) clearly had out-of-sample prediction in mind:

In other words, given some choices A, constraint is our ability to predict other choices B. It would not make sense to be given choices A and measure constraint as our ability to predict A with itself. An out-of-sample measure of constraint is more consistent with the notion that belief systems and ideologies are bundles of ideas, structured together through the common policy space.

Second, on methodological grounds, in-sample estimates of fit are biased toward measuring higher constraint and higher dimensionality. More complex models tend to overfit to training data (Hastie, Tibshirani, and Friedman Reference Hastie, Tibshirani and Friedman2009). Even if political preferences are low-dimensional, higher-dimensional ideal point models will tend to overfit and thus overstate the true dimensionality of preferences. The threat of overfitting is quite real in our data, and we present ample evidence of this in Section 5.

3.2 Out-of-Sample Validation for Ideal Point Models

To measure out-of-sample predictive power, we must have some data that are not in the sample used to fit the ideal point model parameters. A natural first reaction would be to simply drop some actors or some votes from the analysis, and then predict choices for those actors or votes. However, every actor and every vote in the ideal point model has a parameter that must be modeled—namely, $\alpha _{j}, \beta _{j}$ for votes and $\gamma _{i}$ for actors—so we cannot exclude whole actors (rows) or whole votes (columns) from the model fitting process.

Our proposed validation scheme gets around this obstacle by randomly selecting actor-vote pairs, corresponding to individual cells the in data matrix Y, and hiding them from estimation. If we only randomly remove a few cells—perhaps 10% of the matrix Y—then almost all of any actor’s choices will still be available for learning $\gamma _{i}$ . Similarly, we will still have roughly 90% of the choices for vote j, so the vote parameters $\alpha _{j}, \beta _{j}$ can still be estimated with ease. With estimates of these parameters in hand, we can go back and evaluate how well the ideal point model can explain the held-out choices (cells). Figure 1 illustrates the hold-out strategy.

Figure 1 An illustration of our out-of-sample validation strategy with $N = 8$ actors and $J = 5$ votes. Cells are randomly sampled to be in the test set.

Below, we implement two versions of this cell hold-out strategy to perform out-of-sample validation of ideal point models. The first approach is the simple train-test split we described above: one training sample is used to fit the model with 90% of the cells observed and a performance is evaluated on a test sample with the 10% of cells that were randomly held out. A second strategy is a cross-validation approach where we randomly divide all the cells into 10 groups and treat each of the 10 groups as a test sample in 10 different model fits. For each of these 10 model fits, we use the other 9 nontest groups as the training sample.Footnote ⁷ This second approach uses all of the data to estimate out-of-sample performance, since each cell appears exactly once in a test sample.Footnote ⁸

We show in a small simulation study, reported in Figure 4 in Online Appendix C, that the proposed strategy can accurately recover the true dimensionality of the data-generating process with datasets similar in size to those used in this paper.

In terms of identifying the most appropriate number of dimensions, our approach is an application of model selection from statistics and machine learning. We treat each possible dimension D as a separate model and identify the best model based on optimizing a statistic (Hastie et al.  Reference Hastie, Tibshirani and Friedman2009). In our case, that statistic is hold-out accuracy, but we could have also made a case for using other well-established model-selection criteria such as AIC (Akaike Reference Akaike1973), BIC (Schwarz Reference Schwarz1978), etc. We have chosen hold-out accuracy, because it is both substantively more interpretable (how much constraint?) and closer to the original notion of constraint put forward in Converse (Reference Converse and Apter1964). Our substantive conclusions are not sensitive to this choice, as we document in Online Appendix E.

Political scientists have previously sought to validate ideal point models in a variety of ways. The most common strategy has been to focus entirely on in-sample measures of fit (i.e., without a hold-out sample). For example, in their work on congressional roll-call voting, Poole and Rosenthal (Reference Poole and Rosenthal1997) report that in-sample accuracy does not increase beyond two dimensions. Jessee (Reference Jessee2009) presents data supporting the same conclusion for survey respondents.

3.3 Estimating Ideal Point Models

Our proposed cross-validation approach requires refitting a multidimensional ideal point model on each dataset 10 separate times. To do this quickly while allowing for large amounts of missing data (due to item nonresponse), we wrote software based largely on the formulas of Imai, Lo, and Olmsted (Reference Imai, Lo and Olmsted2016).Footnote ⁹ It is described in detail in Online Appendix A and is available online.Footnote ¹⁰ $^{,}$ Footnote ¹¹ Also in Online Appendix B, we show that our one-dimensional ideal point estimates are highly correlated with one-dimensional DW-NOMINATE scores ( $r = 0.97$ ) for members of Congress (Poole and Rosenthal Reference Poole and Rosenthal1997) and Shor–McCarty scores ( $r = 0.86$ ) for state legislators (Shor and McCarty Reference Shor and McCarty2011).

4.1 Senate Voting Data

As a benchmark, we use roll-call votes from the 109th Senate (2005–2007). These data are included in the R package pscl and contain 102 actors voting on 645 roll calls. About 4% of the roll-call matrix is missing.

4.2 NPAT

As a source of survey data among elites, we use data from Project Votesmart’s National Political Courage Test, formerly known as the National Political Awareness Test (NPAT). The NPAT is a survey that candidates take. The goal of the survey is to have candidates publicly commit to positions before they are elected. For political scientists, the data are useful, because they provide survey responses to similar questions across institutions. As such, one prominent use of the NPAT data is to place legislators from different states on a common ideological scale (Shor and McCarty Reference Shor and McCarty2011).

While there are some standardized questions, question wordings often change over time and across states, requiring researchers to merge together similar questions. The full matrix we observe has 12,794 rows and 225 columns. Unlike the roll-call data, however, there is a high degree of missingness: 79% of the response matrix is missing.

4.3 Paired Survey of State Legislators and the Public

We additionally use Broockman’s (Reference Broockman2016) survey of sitting state legislators. This survey contains responses from 225 state legislators on 31 policy questions. Question topics include Medicare, immigration, gun control, tax policy, gay marriage, and medical marijuana, among others. Only about 5% of the response matrix is missing. Additionally, we use a paired survey of the public that is also reported in Broockman (Reference Broockman2016). A subset of the questions are identical to those asked of state legislators. We only use the first wave of the survey, in which there are 997 respondents and no missing data.

4.4 2012 ANES

We use questions from the 2012 American National Election Studies Time Series File, drawn from the replication material of Hill and Tausanovitch (Reference Hill and Tausanovitch2015). There are 2,054 respondents and 28 questions. These questions cover a broad swath of politically salient topics, including health insurance, affirmative action, defense spending, immigration, welfare, and LGBT rights, as well as more generic questions about the role of government. About 10% of the response matrix is missing. We also use various subsets of the American National Election Study (ANES) to investigate heterogeneity in the public.

4.5 2012 CCES Paired Roll Call Votes

Finally, we use data from the 2012 Cooperative Congressional Election Survey. In particular, we focus on the “roll-call” questions, where respondents are asked how they would vote on a series of bills that Congress also voted on. These data have been used to jointly scale Congress and the public (Bafumi and Herron Reference Bafumi and Herron2010). There are 54,068 respondents, answering 10 such questions on the 2012 CCES. The questions cover bills such as repealing the Affordable Care Act, ending Don’t Ask Don’t Tell, and authorization of the Keystone XL pipeline. Only about 3% of the response matrix is missing.

We also match these survey responses to the corresponding roll-call votes in the Senate. These votes took place in the 111th, 112th, and 113th Congresses. We are able to match nine questions to roll-call votes.Footnote ¹² A full list of the votes used for scaling is available in Online Appendix D.

6.1 Constraint Among Elites and the Public

The main results are shown in Figure 3. The left-hand panel plots the average cross-validation accuracy for each dataset. The right-hand panel plots the increase in accuracy for $D \in \{1, \dots , 5\}$ compared to the intercept-only model.

Figure 3 (Left) Cross-validation accuracy for models up to five dimensions. (Right) Increase in percent of accurately classified votes compared to an intercept-only model. Error bars show 95% confidence intervals, clustered at the respondent level.

Beginning at the top of the figures, the solid squares show the cross-validation accuracy of ideal point models for roll-call votes in the 109th Senate. The left-hand panel shows that nearly 90% of votes are correctly classified by a one-dimensional ideal point model. The right-hand panel shows that this is about a 20 percentage point increase over the intercept-only model. As discussed in the previous section, there is little additional gain in accuracy for the Senate data moving beyond a single dimension, though the out of sample performance does not degrade either.

Next, the hollow square shows the results when applied to data from Broockman’s (Reference Broockman2016) survey of state legislators. A one-dimensional model can accurately classify roughly 83% of responses. Again, this is an increase of over 20% percentage points compared to the intercept-only model. Here, the performance of the model begins to decay once we estimate more than a single dimension. This result again underscores the unidimensionality of political constraint among political elites.

The one-dimensional model performs less well when applied to the NPAT data, as illustrated by the solid diamonds. A one-dimensional model correctly classifies only about 75% of responses—an increase of less than 10 percentage points over the intercept-only model. This increase is less than half of the gain achieved with the other two sources of elite data. There is a mild increase in accuracy associated with a second dimension, though the increase is only about 2 percentage points.Footnote ¹⁷

Notwithstanding the NPAT results, the picture that emerges from this exercise confirms the conventional wisdom that politicians—at both the national and state level—are highly constrained in their preferences. Two-thirds of inexplicable votes under the null model are now predictable due to the inclusion of a one-dimensional ideal point.

Such a dramatic increase does not hold for the public. As noted above, we use data from the 2012 ANES and CCES. The nature of the questions included differs between these sources. For the ANES, the questions are typical of public opinion research. The CCES questions, however, ask respondents how they would vote on particular roll-call votes that were actually voted on in Congress. Despite the differences in question format, our substantive conclusions are identical for both datasets.

Consider the solid circles in Figure 3, which correspond to the full sample of ANES respondents. The left-hand side shows that an intercept-only model correctly classifies about 62% of responses. Adding a one-dimensional ideal point increases this classification accuracy to about 69%. Similarly, an intercept-only model correctly classifies about 63% of CCES roll-call responses, compared to 71% accuracy for the one-dimensional model. In both cases, additional dimensions do not increase the performance of the models and, in the case of the CCES, degrade the performance.

These results suggest that classification accuracy increases by about 12% in a one-dimensional model compared to an intercept-only model.Footnote ¹⁸ Despite using a different methodology, Lauderdale et al. (Reference Lauderdale, Hanretty and Vivyan2018) come to a similar conclusion; they report that about one-seventh of the variation in survey responses can be explained by a one-dimensional ideal point, while the rest they attribute to idiosyncratic or higher-dimensional preferences.

Overall, we take these results to mean that there is some constraint in the public, but the relationship between the estimated ideal points and the survey responses is much noisier among the public than it is among elites. For the ANES and CCES, a one-dimensional ideal point model only increases classification accuracy by about 7 or 8 percentage points compared to an appropriate null model. Only about 20% of unpredictable votes under the null model are now predictable using ideal point models. This number pales in comparison to the 67% of inexplicable-turned-predictable votes for the national and state political elites.

6.2 Investigating Heterogeneity in the Public

Of course, there is heterogeneity in the level of constraint in the public, and the overall results may mask constraint among a meaningful subset of the public. As a preliminary test of this possibility, we rerun the ANES analysis after subsetting to people who say self-identify as ideological (i.e., answer 1, 2, 6, or 7 on a 7-point ideology scale). This group of people is likely to have better-formed opinions about political issues and to perceive a common policy space, implying that we may observe more constraint in this population. These results are shown in the solid triangles in Figure 3. As expected, ideal point models have higher accuracy among this subset than among the ANES respondents as a whole. A one-dimensional model can correctly classify 73% of responses among this subset, compared to only 60% that are correctly classified by the intercept-only model. The right-hand panel also shows that the absolute increase in accuracy is actually larger than the increase for the NPAT. Still, compared to the Senate roll-call votes or the state legislator survey, the increase in accuracy is relatively small, again highlighting the higher level of constraint among elites than the public.

A fuller picture is presented in Figure 4, which shows the average increase in classification accuracy for each respondent from a one-dimensional model, relative to the intercept-only model, across a number of political and sociodemographic variables. The black points show the results when the cross-validation procedure is run on the full dataset, while the gray points show results when it is run on each subset separately.Footnote ¹⁹ The political variables include whether the respondent was contacted by or donated to a campaign, the respondent’s self-report ideology, party identification, and whether the respondent correctly places the Democratic Party to the left of the Republican Party on an ideology scale (Freeder et al.  Reference Freeder, Lenz and Turney2019). The socioeconomic variables include age, education, gender, family income, and race.

Figure 4 Constraint among subsets of the public. The points show the average respondent-level increase in classification accuracy obtained by a one-dimensional ideal point model relative to the intercept-only model. Bars show 95% confidence intervals. The black points show results when all respondents are used in the cross-validation procedure, while the gray points show results when cross-validation is performed on each subset separately. “Placement knowledge” refers to whether respondents place the Democratic Party to the left of the Republican Party on a 7-point ideology scale (Freeder et al.  Reference Freeder, Lenz and Turney2019).

The results suggest that there is indeed heterogeneity in the public. Broadly, we find significantly more constraint among conservatives than liberals, Republicans than Democrats, and those who are more knowledgeable and engaged with politics. Similarly, we find greater constraint among people who are older, more highly educated, and richer.

Nonetheless, only in a few subgroups—namely, conservatives and Republicans—does the increase in out-of-sample predictive accuracy come close to the increase seen among politicians.Footnote ²⁰ For the vast majority of subgroups we study, a one-dimensional ideal point model does help predict responses better than an intercept-only model, but the gains are very modest in comparison to politicians.

6.3 Explaining the Public-Politician Divide

Our results thus far suggest that ideal point estimates extract relatively little information from survey responses of the mass public—at least when compared to politicians. Our preferred interpretation is that the public simply has a lower degree of ideological constraint than political elites.

But there are at least three alternative explanations that we probe in this section. The first is that surveys and roll-call votes are very different environments. Survey respondents face few incentives to thoughtfully consider their responses before answering, which may lead to an increased amount of noise in their responses. In contrast, roll-call votes in Congress are “real-world” actions that provide obvious incentives to vote in particular ways.

Second, even if one grants that survey respondents reveal genuine preferences, one might object on the grounds that the set of topics covered in the datasets are not the same. If roll-call votes in Congress are simply better tools for discriminating ideology than survey questions, we would overestimate the degree of constraint in Congress relative to the public.

Third, given the results of the previous section showing some evidence of heterogeneity in the public, it could be that the increased constraint among politicians is simply explained by the unrepresentative demographics of politicians.

To assess the plausibility of these hypotheses, we take advantage of two paired datasets, in which politicians and the public respond to identical questions. Recall that the CCES questions correspond to roll-call votes that were recently held in Congress. This feature allows us to compare the performance of scaling methods using the exact set of issues in Congress and on the CCES. If differing agendas are the cause of the divergent results above, then we should see the divergence in constraint between the public and political elites shrinks when restricting ourselves to a common agenda. Additionally, we can run the analysis on both the full set of CCES respondents as well as a subset that is selected to mirror—to the extent possible—the demographics of the Senate.Footnote ²¹ If either the agenda or demographics explain our results, then this sample should show a similar degree of constraint as Senate roll-call voting.

The left-hand panel of Figure 5 shows the roll-call measures for the Senate and the CCES, for both the full sample and the sample matched to Senate demographics. Despite including only 8 roll-call votes in the Senate, a one-dimensional model accurately classifies nearly 90% of votes—compared to less than 60 in the intercept-only model. In contrast, the accuracy among the public on the same questions goes from 63% to 71% in the full sample. The CCES sample that is demographically matched is somewhere in between, with accuracy increasing from 63% in the intercept-only model to 79% in the one-dimensional model. This finding provides confirmation of the prior result that there is heterogeneity in the level of constraint across the public. Still, even among this group of respondents who are demographically similar to Senators, their survey responses are less predictable than Senators’ roll-call votes. Some, but not all, of the increased constraint seen among politicians can be explained by their demographics.

Figure 5 Comparison of cross-validation accuracy in the public and among elites, holding the survey items constant. Error bars show 95% confidence intervals, clustered at the respondent level. Even with common agendas and incentives, politicians exhibit a higher degree of constraint than the public.

Finally, returning now to the first objection, if there are different incentives created by the roll-call context, we might still observe differences. To probe this question, we take advantage of a parallel survey of the mass public that Broockman (Reference Broockman2016) conducted along with the state legislator survey. Here, legislators’ responses were anonymous, so the incentive structure inherent to survey-taking is the same for both the mass public and elites.

The results are shown in the right-hand panel of Figure 5. They tell an even more stark story when the survey context is held fixed: politicians’ responses are quite predictable, while the public’s are not. This result suggests that it is not the use of surveys per se that is driving the difference between politicians and the public.

These results suggest that the driving force behind the divergent performance of ideal point models in the public relative to elites is primarily the differing levels of constraint of politicians as politicians—not a different agenda, different incentives faced by actors operating in public and private, nor the demographic characteristics of politicians, although this last element does play a part.