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Coordinating Voting in American Presidential and House Elections by Walter R. Mebane, Jr. y July 21, 1997 y Associate Professor, Department of Government, Cornell University, [email protected]. Building on earlier work (Alesina 1987; 1988; Alesina and Rosenthal 1989), Alesina and Rosenthal (1995) use a unidimensional spatial voting model in which individuals coordinate their votes to explain important political and economic phenomena in the United States, including in particular the midterm loss phenomenon and election-related uctuations in economic growth. Coordination means that an individual's presidential and congressional vote choices are jointly determined. Assuming that each individual's voting strategy satises a condition they call conditional sincerity, Alesina and Rosenthal derive a pivotal voter theorem from which it follows that if the two political parties oer distinct policy positions, then in equilibrium some voters will split their tickets, voting for one party for President but for the other party for the legislature. Alesina and Rosenthal also show conditions under which some voters will switch their votes between the presidential and midterm elections. Such switching, they argue, can explain why the President's party uniformly loses vote share at midterm. Alesina and Rosenthal consider complications due to incumbent advantage, and they derive economic implications in the form of an expected partisan business cycle (1995, 137{203). The latter they test empirically using aggregate time series data (Alesina, Londregan and Rosenthal 1993; Alesina and Rosenthal 1995, 204{242). The theory that Alesina and Rosenthal develop is elegant, and they amass a persuasive body of aggregate time series evidence to support its key predictions. What is missing is micro-level evidence to show that individuals do indeed make their voting decisions in accordance with strategies of the kind that Alesina and Rosenthal posit. In this paper I describe and estimate a probabilistic voting model designed to test whether individuals' votes for President and for the House of Representatives are coordinated as Alesina and Rosenthal's theory suggests they should be. In particular I test for the most immediate consequence of the pivotal voter theorem, which is that each voter should use a cutpoint strategy (Alesina and Rosenthal 1995, 77, 111{113). With the spatial competition assumed to be occurring 1 over a continuous set of liberal-to-conservative policy alternatives, mapped onto the unit interval [0; 1], the assertion is that the interval contains two cutpoints, ^ and ~. An individual whose policy bliss point is less than ^ always votes for the Democratic candidate for President while someone whose bliss point is greater than ^ always votes for the Republican. Someone whose bliss point is less than ~ always votes Democratic in the legislative election while someone whose bliss point is greater than ~ always votes Republican. When ^ 6= ~, the theorem says that individuals whose bliss points fall between the two cutpoints will split their tickets between the two parties. In the probabilistic coordinating voting model developed in this paper, someone whose bliss point is less than ^ has a greater probability of voting for the Democratic presidential candidate than does someone whose bliss point is greater than ^, but the vote choice is not certain to be for the Democrat. Votes for House candidates are likewise probabilistic. I assume that the cutpoints themselves are random variables about which each individual has a subjective probability distribution. Each person's probabilistic coordinating voting behavior occurs relative to the expected values the cutpoints have according to the person's subjective distribution for them. I do not assume that the dierences between an individual's bliss point and the expected cutpoints are the sole determinants of her vote choices. The individual's partisanship and evaluation of the economy also aect the choices, as do spatial comparisons not mediated by the cutpoint values. House votes are also aected by whether the incumbent is running for reelection. I augment the specication of coordinating voting with one idea about the substantive content of coordination that is not considered in Alesina and Rosenthal's (1995) theory. The idea is that someone who believes the economy is poor or getting worse may coordinate in a dierent way than does someone who thinks the economy is in great shape. The person with the negative view may be more likely to wish to see government policy pushed in a more expansive direction|to see active steps taken to create jobs and to provide help for those encountering bad luck during the 2 tough period. Someone who does not believe that the economic situation is so dire may instead believe that the usual American norm of personal economic responsibility (Brody and Sniderman 1977; Schlozman and Verba 1979) should apply and so favor a more restricted range of government actions. Someone who has a negative view of the economy may therefore coordinate his votes in a way that favors Democratic candidates|one or both cutpoints may be shifted upward|while the economic optimist may coordinate in a way more favorable to Republican candidates. In this paper I examine votes only in presidential election years, using data from the American National Election Studies (ANES) Pre- and Post-Election Surveys of 1980, 1984, 1988, 1992 and 1996. The analysis tests Alesina and Rosenthal's predictions regarding on-year coordinating voting but not their predictions about vote switching between presidential and midterm years. Subjective Cutpoint Distributions Using the pivotal voter theorem, Alesina and Rosenthal (1995, 96) show the legislative and presidential cutpoints to be related to one another according to ~ = P (^) 1 +RK + (1 , P (^)) 1D++KK (1) where R and D are the policy positions of the two parties (0 D R 1), P (^) is the probability that the Republican presidential candidate wins given the presidential cutpoint ^, and K = (1 , )(R , D ) for some 2 (0; 1). In Alesina and Rosenthal's theoretical development, \ represents the weight of the president in policy formation" (1995, 47). If = 1, the president dictates policy and the legislature plays no role. If = 0, the legislature determines policy and the president is irrelevant. Using ~R = R =(1 + K ) and ~D = (D + K )=(1 + K ), equation (1) becomes ~ = P (^)(~R , ~D ) + ~D : (2) The presidential cutpoint satises the constraint ~D ^ ~R . 3 I treat the party policy positions, the cutpoints and the probability that the Republican presidential candidate wins all as subjective and therefore as potentially varying across individuals. Each individual i may have a distinct belief about the policies likely to ensue given a Democratic rather than a Republican President. Each individual acts in response to subjective values ~Ri and ~Di , 0 ~Di ~Ri 1, rather than in response to a pair of universally shared values ~R and ~D . Such variation may occur because individuals may have diering beliefs about the relative power of the presidential and legislative institutions. In this case, i varies over individuals so that Ki = (1 , i )(R , D ), ~Ri = R =(1 + Ki) and ~Di = (D + Ki )=(1 + Ki). Or individuals may have diverse beliefs about the party policy positions. For instance, beliefs may vary because of variations across legislative districts in the policy positions taken by elected party representatives. Individuals do not know the exact values of the cutpoints, but rather make their choices based on their beliefs about the cutpoints' statistical distributions. Individual i believes that the presidential cutpoint has a continuous distribution function on the interval [~Di ; ~Ri ], with probability density R f^ i (^) > 0 for all ^ 2 [~Di ; ~Ri ] and ~~DiRi f^ i (^)d^ = 1. In particular, I assume that each individual treats ^ as having a beta distribution dened by f^ i (^) = fGi (gi (^)), where gi (^) = (^, ~Di )=(~Ri , ~Di ) and fGi is a beta density on [0; 1], namely fGi (g ) = g Gi ,1(1 , g)Gi ,1 =B ( 0g1; Gi ; Gi ); where Gi > 0, Gi > 0, and B ( ; ) denotes the beta function with arguments and . For individual i the presidential cutpoint ^ is therefore distributed beta ( Gi ; Gi ) on [~Di ; ~Ri ]. The cutpoint value that individual i uses for making voting decisions is the expectation Z ~Ri ^i = ~ ^f^ i (^)d^ "Di # Z gi (~Ri ) = gi(^)fGi (gi (^))dgi(^) (~Ri , ~Di) + ~Di gi (~Di ) = gi(~Ri , ~Di ) + ~Di (3) 4 R where gi = 01 gfGi (g )dg . In order to minimize the losses it expects from errors in predicting ^, each individual i should choose the form for f^ i that has the smallest variance for a given value of ^i . Among beta densities, the minimum variance occurs if f^ i is unimodal.1 f^ i is unimodal if fGi is unimodal, and fGi is unimodal if Gi > 1 and Gi > 1. I use Gi = exp(b1xi + b2) + 1 and Gi = exp(b2) + 1, where xi is an observed variable and b1 and b2 are coecients.2 Similarly to Alesina and Rosenthal's formulation, an expected legislative cutpoint ~i for individual i is determined jointly with the expected presidential cutpoint ^i . In the present model the cutpoints are related to one another through the density f^ i and a function Pi (^) that represents the subjective (according to i) conditional probability that the Republican candidate will win, given a presidential cutpoint at ^. Individual i computes Pi (^) by integrating over the range of voters that ought to be voting for the Republican presidential candidate given ^. The subjective distribution of voter bliss points over which i integrates is a beta ( Vi ; Vi ) distribution on [0; 1], with Vi > 0, Vi > 0 and density fVi (v ) = v Vi ,1 (1 , v )Vi ,1 =B ( Vi ; Vi ) for 0 v 1. I dene R Pi (^) = ^1 fVi (v)dv. Because Pi (^) is a decreasing function of ^ for all ^ 2 [0; 1], such a form for Pi satises the requirement that a higher value for the presidential cutpoint should imply a lower probability that the Republican candidate wins (Alesina and Rosenthal 1995, 95). Using a beta distribution for each individual's beliefs about the distribution of voters makes those beliefs compatible with Alesina and Rosenthal's (1995, 73) assumption that there is a continuum of voters described by a cumulative distribution function that is continuous and strictly increasing on (D ; R). The beta distribution generalizes Alesina and Rosenthal's (1995, 86) uniform distribution.3 The value that i uses for the legislative cutpoint is the expected value of Pi (^)(~Ri , ~Di ) + ~Di , with the integration being over the values of ^ that have positive probability according to f^ i , 5 namely Z ~Ri ~i = ~ [Pi(^)(~Ri , ~Di ) + ~Di ]f^ i (^)d^ Di = Pi (~Ri , ~Di ) + ~Di ; (4) R~ where Pi = ~DiRi Pi (^)f^ i (^)d^. Notice that equation (4) has the same form as equation (2). I assume that each individual's subjective distribution for voters' preferences is compatible with the individual's subjective distribution for the presidential cutpoint, in the sense that if fVi places the bulk of voters in some range (Vi ; Vi ), then by fGi it is highly likely that the transformed presidential cutpoint gi (^) is in that same range.4 Such a compatibility assumption follows naturally from the idea that each individual i believes both that the set of voters capable of deciding the presidential election is contained in the interval [~Di ; ~Ri ], and that all voters are using cutpoint strategies. I assume that fGi and fVi have the same mode. Letting Vi = exp(b3xi )+1 and Vi = 1, with xi being the same as in Gi , I impose the assumption by specifying that b3 = b1.5 The Coordinating Structure A key property of the \stable conditionally sincere" equilibria for Alesina and Rosenthal's models is that the voter whose bliss point i equals the legislative cutpoint ~ is indierent between the parties in the legislative election, and likewise the voter whose bliss point equals the presidential cutpoint ^ is indierent between the parties in the vote for President (Alesina and Rosenthal 1995, 73{82, 107-117). I impose analogous indierence requirements in the present model. If i equals the expected legislative cutpoint ~i , then the coordinating structure has no eect on individual i's vote for a House candidate, and if i equals the expected presidential cutpoint ^i , then the coordinating structure has no eect on individual i's presidential vote. 6 Dene the coordinating structure as the set wi = fwiRR; wiDR; wiRD ; wiDD g, where wiRR = aP (i , ^i) + aH (i , ~i ) wiDR = aP (^i , i) + aH (i , ~i ) , aPH (i , ^i )(i , ~i ) wiRD = aP (i , ^i) + aH (~i , i ) , aPH (i , ^i )(i , ~i ) wiDD = aP (^i , i) + aH (~i , i ) with aP 0, aH 0 and aPH 0 being constant coecients. The probability jk i that i votes for party j 2 fD; Rg for President and party k 2 fD; Rg for the House is a function of vijk = wijk + zijk , where zijk includes factors that aect the vote choice in addition to the coordinating structure. I assume that jk i is multinomial, with jk i = exp vijk ; exp viRR + exp viDR + exp viRD + exp viDD Using vote indicator variable yPi = 1 if i votes for the Republican presidential candidate, = 0 if i votes for the Democrat, and yHi = 1 if i votes for the Republican House candidate, = 0 if i votes for the Democrat, the likelihood for i is6 y y DR (1,y )y RD y (1,yHi )(DD )(1,yPi )(1,yHi ) : Li = (RR i ) Pi Hi (i ) Pi Hi (i ) Pi i The coordinating structure species that, net of the eects represented by the zijk terms, a split-ticket vote is most likely when an individual's bliss point i is between the two cutpoints. Suppose the zijk terms are all zero. Then if aP = aH > 0, the odds (DR + RD )=(RR + DD ) of a split ticket are maximized at i = (^i + ~i )=2. The value of i that maximizes the odds of a split ticket is closer to ^i if aP > aH and closer to ~i if aH > aP , but the maximizing value always falls between ^i and ~i . Because log(DR =RD ) = 2[aP (^i , i ) + aH (i , ~i )] + ziDR , ziRD , the content of a split vote depends on the relative position of the cutpoints, sharply so if aP and aH are large. If ^i > ~i , then a split vote by i is more likely to be for the Democratic presidential candidate and 7 a Republican House candidate, while if ~i > ^i the vote is more likely to be for the Republican presidential candidate and a Democratic House candidate. Data To estimate the model I use data from the ANES Pre-/Post-Election surveys of 1980, 1984, 1988, 1992 and 1996 (Miller and the National Election Studies 1982; 1986; 1989; Miller, Kinder, Rosenstone and the National Election Studies 1992; Rosenstone, Kinder, Miller and the National Election Studies 1997). For the current analysis I pool the cross-sections from all ve years. To measure bliss points i and policy positions ~Di and ~Ri , I use survey items that ask each respondent to place self, Republican party and Democratic party on seven-point scales referring either to liberal-conservative ideology or to a policy issue. The single policy dimension in Alesina and Rosenthal's model is supposed to summarize all possible grounds for electoral competition, so I use as broad range of scale items as possible.7 In each year I use every scale for which survey respondents were asked to place themselves and the two parties. To combine the scales into single variables, I use the idea that it is relative rather than absolute positions that matter for the coordinating voting model. What matters for each self placement item is the proportion of the population that would support each of the seven possible positions. I assume that the items are, at least to a rough approximation, stochastically ordered relative to a common underlying distribution of positional preferences. I use the cumulative distributions observed for each set of three scales to compute numerical codes for the response categories. By the logic of Alesina and Rosenthal's theoretical analysis, such codes are comparable across issues, because the theory depends only on the parties' locations relative to the distribution of voters. The Appendix lists the items used for each survey and describes in more detail the method used to scale the responses into the [0; 1] interval. I assume that the survey responses reect individuals' 8 beliefs about the powers of the President and the Congress, so that the observed party position data are ~Di and ~Ri rather than Di and Ri . For each individual the value of each bliss point or party position variable is an average taken over all the items to which the individual responded. To measure vote choices I use the post-election choices reported by individuals who said they voted. In the zijk terms I include a set of dummy variables to measure partisanship, a variable to measure retrospective evaluations of the national economy, dummy variables to measure whether a Democratic or Republican incumbent is running for reelection or whether there is an open seat, and a dummy variable for each year. The incumbent status variables are included in such a way as to aect only the choice between House candidates. I also include measures of the absolute dierences between each individual's bliss point and the positions the individual perceives for the jk Democratic and Republican parties. Using coecients cjk h for h 2 P = fSD,D,DL,I,RL,R,SRg, cm jk for m 2 Y = f84,88,92,96g, cjk E , c1, c2 , c3 , c4, c5 and c6, the zi terms are X DR X DR ch PID hi + cm YRmi + cDR E PRESi ECi + c1ji , ~Di j + c2 ji , ~Ri j h2P m2Y X X RD ziRD = cRD cm YRmi + cRD E PRESi ECi + c3ji , ~Di j + c4 ji , ~Ri j h PID hi + h2P m2Y ziDR = + c5IDEMi + c6 IREPi ziDD = X DD X DD ch PIDhi + cm YR mi + cDD E PRESi ECi + c1ji , ~Di j + c2ji , ~Ri j h2P m2Y + c3ji , ~Di j + c4 ji , ~Ri j + c5IDEMi + c6 IREPi with ziRR = 0 to normalize the coecients. PIDSD i , PIDD i , PIDDL i , PIDI i , PIDRL i , PIDR i and PIDSR i are the partisanship dummies.8 YR84i , YR88i , YR92i and YR96 i are dummy variables for each indicated year. ECi measures economic evaluations.9 PRESi changes sign depending on the incumbent President's party: PRESi = 1 if Republican; = ,1 if Democrat. I use the RD DD product PRESi ECi so that cDR E , cE and cE should all be negative: if voters are using a simple 9 retrospective calculus keyed to the incumbent President, then an increase in PRESi ECi should increase the chances of voting for the Republican candidate. Dummy variables IDEMi and IREPi measure incumbent status. IDEMi = 1 if a Democratic incumbent is running for reelection in individual i's congressional district, while IREPi = 1 if a Republican incumbent is running for reelection there. If both IDEMi = 0 and IREPi = 0, the district has an open seat.10 In the beta densities fGi and fVi , xi is ECi and b1 and b2 are parameters to be estimated. A value of b1 < 0 would support the idea that an individual who thinks the economy is getting worse (ECi < 0) coordinates her votes in a way that more strongly favors Democratic presidential candidates, while someone who believes the economy is getting better (ECj > 0) coordinates in a way that more strongly favors Republicans. If b1 < 0, then gi > gj , so that if individuals i and ~ ~ j place the parties in the same locations (~Di = ~Dj < ~Ri = ~Rj ), then ^i > Di +2 Ri ^j . The economic pessimist, i, has an expected presidential cutpoint greater than that of the economic optimist, j . The conditions under which the pessimist will also have a legislative cutpoint greater than that of the optimist are more complicated, as the result depends on the values of b1 , b2, ~Di and ~Ri .11 Estimation and Test Results Estimation is by maximum likelihood, using only individuals who have ~Di < ~Ri and who voted for either the Democratic or Republican candidate in both the presidential and House races.12 Table 1 reports the maximum likelihood estimates (MLEs) for the parameters. The likelihood ratio test statistic for the signicance of the coordinating structure is X^ 2 = 15:86. Using the 25 distribution, the null hypothesis that the coordinating structure makes no dierence gives prob(X 2 > X^ 2) < :01. Clearly the coordinating structure matters.13 *** Table 1 about here *** 10 The coordinating pattern depends strongly on the individual's evaluation of the national economy. The MLE for b1 is a hefty ^b1 = ,7:10. By a one-tailed t-test, the estimate is signicantly negative. The eect the negative value of b1 has on the beta densities fGi (presidential cutpoint) and fVi (voter location) can be seen in Figure 1. When the evaluation of the economy is \much worse," both densities have probability mass concentrated on high values. The voter location density is practically a point mass for the value v = 1:0. As the evaluation of the economy improves through \worse" and \same" to \better," the densities atten out, in the direction of uniformity. The density for an economic evaluation of \much better" is in each case not noticeably dierent from the the density for \better." *** Figure 1 about here *** For most values of ~Di and ~Ri , the estimated densities imply that the cutpoints vary in the expected way as the economic evaluation varies, albeit with one signicant deviation. The plots in Figure 2 illustrate the typical pattern. Figure 2 shows the probabilities RR , DR , RD and DD simulated for each bliss point value in the unit interval, with ~Di = :2, ~Ri = :8 and z RR = zDR = z RD = zDD = 0. For an economic evaluation of \better," the expected presidential cutpoint is ^i :5 while the expected legislative cutpoint is ~i :4 (Figure 2(a)). As one would expect given the similarity of the densities in Figure 1, the same result occurs for an economic evaluation of \much better" (not shown). When the evaluation of the economy decreases to \same," the expected presidential cutpoint does not change but the expected legislative cutpoint increases to ~i :5 (Figure 2(b)). Upon a further decrease of the evaluation, to \worse," the expected presidential cutpoint increases to ^i :55, but the expected legislative cutpoint increases more, to ~i :6 (Figure 2(c)). When the evaluation reaches the maximum of pessimism, with the individual saying that over the past year the economy has become \much worse," the expected presidential cutpoint increases to ^i :73, but the expected legislative cutpoint plummets to ~i :38 (Figure 2(d)). 11 *** Figure 2 about here *** The simulated probabilities in Figure 2 illustrate three characteristic features of the coordinating structure. First, the coordinating structure has no eect on an individual's vote for an oce when the individual's bliss point equals the expected cutpoint for that oce. If the bliss point equals DR DD RD the expected presidential cutpoint (i = ^i ), then RR i = i and i = i , and if the bliss DR RR RD point equals the expected legislative cutpoint (i = ~i ), then DD i = i and i = i . The reason why all four probabilities are equal in Figure 2 whenever the bliss point equals the expected presidential cutpoint is that the MLE for aH is the boundary value ^aH = 0. The second feature is RD that for bliss points between the expected cutpoints, DR i > i when the expected presidential DR cutpoint is greater than the expected legislative cutpoint, but RD i > i when the expected presidential cutpoint is less than the expected legislative cutpoint. Third, the probability of a split ticket vote increases as the distance between the expected cutpoints increases. In Figure 2, the probability of a split ticket vote signicantly exceeds the highest probability for a straight ticket vote only in Figure 2(d), where the evaluation that the economy has become \much worse" induces a fairly wide separation between ^i and ~i . Figure 3 shows that, throughout the data from all ve election years, widely separated cutpoints occur only for individuals who say the economy has become \much worse." Without exception, these people have ^i > ~i . For these people the most likely split ticket vote, at least as far as the coordinating structure is concerned, is for a Democratic presidential candidate and a Republican candidate for the House. Of course, the contributions to the vote choice from the coordinating structure may well be outweighed by the eects of the factors in ziDR , ziRD and ziDD . In any case, in view of the magnitudes estimated for the coordinating structure coecients, coordinating voting cannot be expected substantially to increase the chances of split ticket voting by voters who do not hold to a seriously negative reading of recent economic performance. The largest dierence 12 between expected cutpoints for those who evaluate the economy as \better" or \much better" is ^i , ~i =.16. The univariate, normal-theory 95% condence intervals for the coordinating structure coecients are :03 aP 1:42, 0 aH 0:55, and :90 aPH 5:65. Using the upper bounds for each of these intervals and, for instance, i = :5, ^i = :58 and ~i = :42, would give a value of wi = f,:07; :19; ,:12; :07g for the coordinating structure, a value easily outweighed by factors in ziDR , ziRD and ziDD . *** Figure 3 about here *** The Democrats' Dilemma The pattern of coordinating voting that depends on an individual's evaluation of the economy creates a major dilemma for Democratic candidates. The coordinating voting pattern implies that voters punish a Democratic President for success in improving the economy. Figures 4 and 5 show simulations of the vote in which, unlike Figure 2, the factors in ziDR , ziRD and ziDD are not all set to zero. Results appear for ve of the levels of partisanship. In Figure 4 the evaluation of the economy is \much worse" while in Figure 5 the evaluation is \much better." The values used for the party policy positions are ~Di = :2 and ~Ri = :8. The simulated eects include the eects of the terms of ziDR , ziRD and ziDD that involve the absolute dierences ji , ~Di j and ji , ~Rij.14 Each gure shows probabilities simulated once assuming that a Republican is President and once assuming that the President is a Democrat. Because of the use of the product PRESi ECi in estimating the direct eect of economic evaluations, the probabilities for a Republican President with a \much worse" economy are quite similar to the probabilities for a Democratic President with an economy that is evaluated as \much better." Likewise, the probabilities for a Democratic President with a \much worse" economy are similar to the probabilities for a Republican President with an economy rated as \much better." Indeed, the coordinating structure is the only reason 13 why the respective sets of probabilities are not identical. As previously discussed, the expected cutpoints are not the same for the two dierent evaluations of the economy. In going from an evaluation of \much worse" to one of \much better," the expected legislative cutpoint increases slightly, from ~i :38 to ~i :4, while the expected presidential cutpoint drops dramatically, from ^i :73 to ^i :5. *** Figures 4 and 5 about here *** Figure 6 shows the magnitude of the electoral problem that the coordinating pattern implies for Democratic Presidents. The gure shows two sets of dierences between the simulated probabilities of Figures 4 and 5. In the left column of Figure 6, the probabilties for a Republican President with an economic evaluation of \much worse" are subtracted from the probabilities for a Democratic President with an economic evaluation of \much better." In the right column, the probabilties for a Democratic President with an economy evaluated as \much worse" are subtracted from the probabilities for a Republican President with an economic evaluation of \much better." The point of these values is to illustrate what happens to individuals' voting probabilities when an economically unsuccessful President of one party is succeeded by a President of the other party who enjoys better economic results. Presumably, in that case, many individuals who judged the economy to be in severe decline at the time of the election in which the economically unsuccessful President was turned out of oce will have converted to have a much more favorable view of how things are going at the time when the seemingly more skillful successor stands for reelection. *** Figure 6 about here *** Figure 6 shows that a Democratic President who delivers economic results that voters nd to be much better than what occurred with an economically unsuccessful Republican predecessor for the most part loses rather than gains electoral support. Among voters who have liberal policy preferences, meaning a bliss point i < :2, the probability DR i of a vote split Democratic-President14 Republican-House-candidate increases very slightly|by about .02. But this seeming gain for the Democratic President is actually a loss, as the increases in DR i are more than oset by decreases in the probability of a Democratic straight ticket vote. In fact what is happening is that the Democrats are losing support in open seat House races. Among moderate and conservative voters (i > :3) the Democrats' situation is even more perversely punitive, as both the straight ticket DR (DD i ) and split ticket (i ) probabilities of a vote for the Democratic President decrease. The losses occur for all kinds of partisans. Among conservative Democrats and moderate Independents, the reduction in the probability of a vote for the Democratic President totals almost .1. In sharp contrast, Figure 6 shows that a Republican President who delivers much better economic performance than an unsuccessful Democratic predecessor for the most part gains rather than loses support. In the left column of Figure 6, the change in the probability RR i of a Republican straight ticket vote is uniformly positive. The probability of a vote split Republican-PresidentDemocratic-House-candidate does not always increase, but when it decreases the reduction is always oset by the increase in RR i . What may be described as the economic bias in the structure of coordinating voting presents a Democratic President with a serious political dilemma. To fail to improve the economy would mean overwhelming electoral defeat. In addition, to pursue economic stagnation would be inherently wrong. Stagnation cannot be a policy goal. But success in increasing growth, expanding employment, raising wages and stabilizing prices would mean losses rather than gains in electoral support. The Democratic President is in a box. The Democratic President can avoid losses only if the voters who rate the economy as having improved also believe that the Democratic party policy position has shifted to the right. Voters must believe that the Democratic party has become more conservative. By the current parameter MLEs, the expected presidential cutpoint for a voter who thinks the economy has improved is 15 ^i (~Di +~Ri )=2, midway between the parties' policy positions. The expected presidential cutpoint for a voter who thinks the economy has seriously declined is quite near the policy position of the Republican party (gi :875). If the policy position of the Republican party remains unchanged between elections, then to avoid a loss from improving the economy, the Democratic President must make moderate and conservative voters believe that the policy position of the Democratic party has shifted a substantial distance toward the position previously taken by the Republican party. To avoid losing support, the Democratic President shift the perceived policy position of the Democratic party to the center, and perhaps somewhat to the right of center. If the Republican party policy position itself shifts to the right, then the Democratic party policy position does not need to change as much to preserve the Democrat's previous level of electoral support. For in this case, the Republican party's rightward movement will help keep (~Di + ~Ri )=2 near the location of the previous expected presidential cutpoint, without the Democratic party's position having to change by as much. But if the Republican party policy position shifts to the left, the Democratic party policy position must shift further to the right than would have been necessary to preserve its support had the Republican position remained unchanged. You are Bill Clinton. It is 1996 and the economy is strong. Your Republican opponent, Bob Dole, is resisting pulls from inside his party to move farther right. Indeed, in some respects he may be edging slightly to the left. You have on your desk a bill that will abolish welfare, mandate workfare, reduce health insurance protection for poor children and cut programs for infant nutrition. Signing the bill will provoke outrage among core Democratic constituencies, who will be appalled by an action they believe will cause one million children to fall into poverty. You suspect that, if you sign the bill, long-time liberal friends and allies who work on children's issues in your administration will resign in protest, condemning you for having caved in to the far right wing of House Republicans. You heave a silent sigh of thanks to Newt Gingrich. Smiling in anticipation, you lift your pen. 16 Appendix To measure an individual's bliss point and perceived positions for the Republican and Democratic parties, I assign codes in the [0; 1] interval to each scale in a collection of sets of three seven-point placement scales and then average over the sets to which the individual responded to all three scales|one for self and one for each party. Table 2 lists descriptions and variable numbers for the survey items used for each year. All items are oriented so that the \liberal" position, normally associated with the Democratic party during the given time period, has the lower number. To determine numerical codes, I start by computing the cumulative response proportions for the three scales for each survey item. Denote the successive proportions for item k (e.g., k = \Liberal/Conservative") by 0 = r0kj r1kj r6kj r7kj = 1, for j 2 fS; D; Rg, respectively for the self, Democratic k + rk + rk )=3. party and Republican party scales. For all m 2 f0; 1; : : :; 7g I compute rmk = (rmS mD mR The numerical code for each of the m 2 f1; : : :; 7g original survey responses on all three scales of type k is rmk = (rmk ,1 + rmk )=2. Table 3 shows the codes computed by this procedure for each survey item. *** Table 2 and Table 3 about here *** 17 Notes 1. Let random variable ^ be distributed beta ( ; ) with mean ^0 = =( + ), 0 < ^0 < 1. In terms of and ^0 the variance is var(^ ) = (1 , ^0 )^02 =( + ^0 ), so that for xed mean ^0 , @ var(^ )=@ = ,(1 , ^0)^02=( + ^0 )2 < 0. Because = (1 , ^0)=^0, increasing for xed ^0 R~ increases . It follows that for any ^i0 = ~DiRi ^f0^ i (^)d^ generated by G0 i < 1 or 0Gi < 1, there is a value G00 i > 1 such that Gi > 1 and ^i = ^i0 but var(^) < var(^0 ) for all Gi > G00 i . 2. The mode is exp(b1xi )=(exp(b1xi ) + 1) (Johnson, Kotz and Balakrishnan 1995, 219). 3. The beta (1,1) distribution is the uniform distribution. 4. Recall that gi(^) maps ^ 2 [~Di ; ~Ri] onto the unit interval [0; 1]. 5. The specication with Vi as in the text and Vi = exp(b4)+1 for unknown coecient b4 is not identied in our data. Identication similarly fails if Vi = exp(b4)+1 and Vi = exp(b3xi + b4 )+1. Because the likelihood depends only on the integral Pi (^), a free parameter b4 is redundant with b2. There is information to identify the variance for only one of the densities, either fVi or fGi but not both. 6. Alesina and Rosenthal (1995, 73) assume that voter utility functions are single peaked and dierentiable and that voter preferences satisfy a Spence-Mirlees single-crossing property. In the present model each individual's expected utility may have these properties, in that the multinomial logit likelihood is compatible with stochastic utility maximizing behavior (McFadden 1974; McFadden 1978; Borsch-Supan 1990). 7. There is evidence that the political parties usually represent the principal opposing bundles of policy positions in American politics (Poole and Rosenthal 1984; 1997). 8. The dummies mark the levels of the standard ANES party identication item: PIDSDi = 1, strong Democrat; PIDD i = 1, Democrat; PIDDL i = 1, independent Democratic leaner; PIDIi = 1, pure Independent; PIDRL i = 1, independent Republican leaner; PIDR i = 1, Republican; and 18 PIDSR i = 1, strong Republican. The ANES variable numbers for each year are 266 (1980), 866 (1984), 274 (1988) and 3634 (1992). 9. For 1980, 1984 and 1988 the question wording is \What about the economy? Would you say that over the past year the nation's economy has gotten better, stayed about the same, or gotten worse?" For 1992 the initial part of the question changed to read, \How about the economy." For 1996 the initial part was \Now thinking about the economy in the country as a whole." The responses are coded \much worse" (,1), \somewhat worse" (,:5), \same" (0), \somewhat better" (.5) and \better" (1). The ANES variable numbers for each year are 150 (1980), 228 (1984), 244 (1988), 3532 (1992) and 960386 (1996). 10. The ANES variable numbers for each year are 740 (1980), 59 (1984), 50 (1988), 3021 (1992, with errors corrected as indicated in the codebook le nes92int.cbk) and 960097 (1996). 11. That the conditions are complicated is clear from # Z ~Ri Pi log(^)f^ i (^)d^ Gi + Gi ) , (Gi ))Pi + ~Di ) Z ~Ri Z 1 + (( Vi + 1) , (1))Pi + log(v )fVi dvf^ i (^)d^ ~ ^ ( " @ Pi = x expfb x g expfb2g (( 1 i ~ @b1 i Ri , ~Di Di where (z ) = d log ,(z )=dz denotes the logarithmic derivative of the gamma function. The terms (( Gi + Gi ) , (Gi ))Pi and (( Vi +1) , (1))Pi are positive but the integrals are both negative. 12. Of those survey respondents with complete data who voted as described in the text, 136 (2.9 percent) had ~Di = ~Ri and 554 (11.8 percent) had ~Di > ~Ri . 13. Adding Jacobson's (1990) measure of challenger quality made no dierence in estimates computed using the data for 1980{92. The LR test statistic for the hypothesis that the quality variable adds nothing is X^ 2 = 4:33, which by the 22 distribution is not signicant. 14. YR84i = YR88i = YR92i = YR96i = IDEMi = IREPi = 0, so the simulations are for probabilites as of 1980 in an open seat House race. 19 References Alesina, Alberto. 1987. \Macroeconomic Policy in a Two-party System as a Repeated Game." Quarterly Journal of Economics 102:651{678. Alesina, Alberto. 1988. \Credibility and Policy Convergence in a Two-party System with Rational Voters." American Economic Review 78:796{806. Alesina, Alberto, John Londregan and Howard Rosenthal. 1993. \A Model of the Political Economy of the United States." American Political Science Review 87:12{33. Alesina, Alberto, and Howard Rosenthal. 1989. \Partisan Cycles in Congressional Elections and the Macroeconomy." American Political Science Review 83:373{398. Alesina, Alberto, and Howard Rosenthal. 1995. Partisan Politics, Divided Government, and the Economy. New York: Cambridge University Press. Borsch-Supan, Axel. 1990. \On the Compatibility of Nested Logit Models with Utility Maximization." Journal of Econometrics 43:373{388. Brody, Richard A., and Paul M. Sniderman. 1977. \From Life Space to Polling Place: The Relevance of Personal Concerns for Voting Behavior." British Journal of Political Science 7:337{360. Jacobson, Gary C. 1990. The Electoral Origins of Divided Government: Competition in U.S. House Elections, 1946{1988. Boulder: Westview. Johnson, Norman L., Samuel Kotz and N. Balakrishnan. 1995. Continuous Univariate Distributions, Volume 2. 2d ed. New York: John Wiley & Sons. 20 McFadden, Daniel. 1978. \Modelling the Choice of Residential Location." In Anders Karlqvist, Lars Lundqvist, Folke Snickars and Jorgen W. Weibull, eds., Spatial Interaction Theory and Planning Models. New York: North-Holland, pp. 75{96. Miller, Warren E., and the National Election Studies. 1982. American National Election Study, 1980: Pre- and Post-Election Survey [computer le]. Ann Arbor, MI: Center for Political Studies, University of Michigan. [original producer]. 2nd ICPSR ed. Ann Arbor, MI: Interuniversity Consortium for Political and Social Research [producer and distributor]. Miller, Warren E., and the National Election Studies. 1986. American National Election Study, 1984: Pre- and Post-Election Survey [computer le]. Ann Arbor, MI: Center for Political Studies, University of Michigan. [original producer]. 2nd ICPSR ed. Ann Arbor, MI: Interuniversity Consortium for Political and Social Research [producer and distributor]. Miller, Warren E., and the National Election Studies. 1989. American National Election Study, 1988: Pre- and Post-Election Survey [computer le]. Ann Arbor, MI: Center for Political Studies, University of Michigan. [original producer]. 2nd ICPSR ed. Ann Arbor, MI: Interuniversity Consortium for Political and Social Research [producer and distributor]. Miller, Warren E., Donald R. Kinder, Steven J. Rosenstone, and the National Election Studies. 1993. American National Election Study, 1992: Pre- and Post-Election Survey [enhanced with 1990 and 1991 data] [computer le]. Conducted by University of Michigan, Center for Political Studies. ICPSR ed. Ann Arbor, MI: University of Michigan, Center for Political Studies, and Inter-university Consortium for Political and Social Research [producers]. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributor]. Poole, Keith T., and Howard Rosenthal. 1984. \U.S. Presidential Elections 1968{80: A Spatial Analysis." American Journal of Political Science 28:282{312. 21 Poole, Keith T., and Howard Rosenthal. 1997. Congress: A Political-economic History of Roll Call Voting. New York: Oxford University Press. Rosenstone, Steven J., Donald R. Kinder, Warren E. Miller, and the National Election Studies. 1997. American National Election Study, 1996: Pre- and Post-Election Survey [Computer le]. 2nd release. Ann Arbor, MI: University of Michigan, Center for Political Studies [producer], 1997. Ann Arbor, MI: Inter- university Consortium for Political and Social Research [distributor]. Schlozman, Kay Lehman, and Sidney Verba. 1979. Injury to Insult: Unemployment, Class and Political Response. Cambridge: Harvard University Press. 22 Table 1: Coordinating Vote Model Parameter Estimates parameter MLE SE b1 {7.10 4.03 b2 {4.17 5.40 parameter MLE SE aP .72 .35 aH .00 .28 aPH 3.27 1.21 cDR SD cDR D cDR DL cDR I cDR RL cDR R cDR SR cDR E cDR 84 cDR 88 cDR 92 cDR 96 cRD SD cRD D cRD DL cRD I cRD RL cRD R cRD SR cRD E cRD 84 cRD 88 cRD 92 cRD 96 2.08 .18 .82 {1.11 {2.00 {2.11 {3.42 {1.14 {.57 {.52 .12 .25 .50 .31 .37 .44 .34 .32 .44 .20 .32 .33 .36 .32 1.01 {.06 .45 {.25 {1.12 {1.25 {1.87 {.26 {.01 {.03 {.04 {1.01 .53 .28 .34 .32 .26 .26 .27 .15 .19 .23 .26 .29 parameter MLE d1 {4.14 d2 4.72 d3 {.89 d4 1.19 d5 1.30 d6 {1.25 DD cSD 3.67 cDD 1.14 D cDD 1.78 DL cDD {.74 I DD cRL {2.56 cDD {2.50 R cDD {3.95 SR cDD {1.37 E cDD {.44 84 cDD {.12 88 cDD {.17 92 DD c96 .34 Note: Maximum likelihood estimates. n = 3644 cases. Log-likelihood = ,2209:95. SE .71 .70 .48 .46 .16 .17 .50 .30 .36 .37 .35 .34 .44 .17 .26 .28 .32 .29 Table 2: Variables Used to Measure Bliss Points and Party Policy Positions year description 1980 Liberal/Conservative Defense Spending Government Services/Spending (reversed) Reduce Ination/Reduce Unemployment Liberal/Conservative Views Government Aid to Minorities Getting Along with Russia Equal Rights for Women Scale Government Guaranteed Job and Living Standard 1984 Liberal/Conservative Placement Liberal/Conservative Government Services/Spending (reversed) Minority Aid/No Aid Involvement in Central America Defense Spending Social/Economic Status of Women Cooperation with Russia Guaranteed Standard of Living/Job 1988 Liberal/Conservative Government Services/Spending (reversed) Defense Spending Government-Funded Insurance Guaranteed Standard of Living/Job Social/Economic Status of Blacks Social/Economic Status of Minorities Cooperation with Russia Women's Rights 1992 Ideological Placement Government Services/Spending (reversed) Defense Spending Job Assurance 1996 Liberal/Conservative Government Services/Spending (reversed) Defense Spending Abortion Jobs/Environment Environmental Regulation variable numbers 267, 278, 279 281, 286, 287 291, 296, 297 301, 306, 307 1037, 1053, 1054 1062, 1073, 1074 1078, 1089, 1090 1094, 1105, 1106 1110, 1121, 1122 119, 120, 121, 131, 132, 133, 135, 136, 137 369, 373, 374 375, 378, 379 382, 385, 386 388, 391, 392 395, 398, 399 401, 404, 405 408, 411, 412 414, 417, 418 228, 234, 235 302, 307, 308 310, 315, 316 318, 321, 322 323, 328, 329 332, 337, 338 340, 345, 346 368, 373, 374 387, 390, 391 3509, 3517, 3518 3701, 3704, 3705 3707, 3710, 3711 3718, 3721, 3722 960365, 960380, 960379 960450, 960462, 960461 960463, 960478, 960477 960503, 960518, 960517 960523, 960536, 960535 960537, 960542, 960541 Note: Variable numbers for 1980{92 refer to data on the \ANES 1948-1994 CD-ROM" release of May, 1995. Table 3: Item Response Scores Used for Each Set of Bliss Point and Policy Position Components year description original 1980 L/C DS GS/S(r) RI/RU L/CV GAtM GAwR ERfWS GGJaLS 1984 L/CP L/C GS/S(r) MA/NA IiCA DS S/ESoW CwR GSoL/J 1988 L/C GS/S(r) DS G-FI GSoL/J S/ESoB S/ESoM CwR WR 1992 IP GS/S(r) DS JA 1996 L/C GS/S(r) DS A J/E ER item response scores 1 2 .0175 .103833 .0158333 .0585 .0606667 .204 .0216667 .0876667 .0103333 .0841667 .0285 .1115 .0381667 .120333 .0956667 .283167 .0408333 .143667 .0908333 .243 .0211667 .12 .0433333 .153 .0421667 .146833 .0348333 .138333 .032 .115667 .0431667 .148 .0401667 .132667 .0386667 .133333 .0206667 .113667 .0395 .151333 .029 .102 .0573333 .169167 .0323333 .110833 .0306667 .104667 .04 .127667 .0446667 .1505 .1135 .302 .0246667 .126667 .0436667 .156667 .0321667 .123667 .0336667 .120667 .0201667 .114333 .033 .132333 .0165 .0808333 .0621667 .285167 .0316667 .126333 .0401667 .1485 3 .250833 .143 .382333 .225167 .229333 .253167 .235333 .469 .2925 .365167 .270833 .31 .300833 .293667 .24 .2985 .264667 .271667 .257 .322167 .2155 .297333 .231833 .228667 .261833 .318333 .468667 .280333 .318 .2825 .2495 .2655 .2965 .218 .5505 .291333 .324833 4 .432833 .298833 .581833 .4645 .421833 .459333 .42 .6645 .485 .440667 .454167 .516833 .517 .485333 .431 .531333 .468333 .4745 .434667 .552167 .4215 .472833 .423333 .452667 .471167 .569833 .6785 .463667 .535333 .524167 .432833 .446833 .506167 .438833 .8275 .527833 .557167 Note: See Table 2 for full identication of the variables. 5 .6315 .517333 .7665 .718667 .633 .685667 .658333 .828833 .680333 .536 .6505 .7115 .727333 .678667 .650167 .757333 .687333 .69 .628833 .765667 .660833 .657333 .6335 .6775 .684667 .7895 .849333 .652 .741833 .754 .631667 .638833 .708333 .693 6 .842333 .751167 .896833 .883833 .852833 .857 .8585 .924667 .842167 .6975 .843833 .858833 .868667 .835 .8295 .889167 .848 .8555 .826667 .8975 .840167 .809333 .806333 .817667 .837 .902167 .930333 .830333 .8805 .8925 .796833 .837333 .8675 .8865 7 .979167 .932333 .973167 .9705 .986167 .9605 .967 .978833 .957167 .889167 .9755 .963833 .962167 .9515 .954 .9695 .956833 .963 .9685 .973667 .958333 .939333 .942833 .938167 .949333 .97 .979333 .963667 .969 .971667 .9355 .974 .968167 .978667 .755 .7625 .903167 .979333 .8975 .975667 Figure 1: Presidential Cutpoint and Voter Densities, by National Economy Evaluation much worse density 0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 presidential cutpoint voter location worse worse 0.8 1.0 0.8 1.0 0.8 1.0 0.8 1.0 0.8 1.0 20 density 0.8 0.4 0 0.0 10 1.2 30 0.0 density 100 10 0 5 density 15 300 much worse 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 presidential cutpoint voter location same same 0.0 1.0 density 0.98 0.94 density 2.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 presidential cutpoint voter location better better 0.85 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 voter location much better much better 1.001 presidential cutpoint density 0.96 0.995 0.92 0.998 0.2 1.00 0.0 density 0.95 density 0.96 0.92 density 1.00 0.0 0.0 0.2 0.4 0.6 presidential cutpoint 0.8 1.0 0.0 0.2 0.4 0.6 voter location Figure 2: Examples of Vote Choice Probabilities Generated by the Coordinating Structure 0.2 0.4 0.8 0.4 1.0 0.0 0.2 0.4 0.6 0.8 1.0 individual’s bliss point (c) Economy is Worse (d) Economy is Much Worse 0.0 0.2 0.4 0.6 0.4 θ̃ 0.0 θ̂ θ̃ 0.2 0.2 probability 0.4 0.6 individual’s bliss point 0.0 probability θ̃θ̂ 0.0 0.6 0.6 0.0 0.2 probability 0.4 0.2 θ̃ θ̂ 0.0 probability 0.6 (b) Economy is the Same 0.6 (a) Economy is Better 0.8 1.0 individual’s bliss point 0.0 0.2 0.4 θ̂ 0.6 0.8 1.0 individual’s bliss point Republican straight ticket Democratic presidential, Republican House candidate Republican presidential, Democratic House candidate Democratic straight ticket Party policy positions are ~D = :2 and ~R = :8. In this gure, ^ denotes the expected presidential cutpoint and ~ denotes the expected legislative cutpoint. Figure 3: Expected Cutpoints Estimated for Individuals in the ANES Presidential Year Samples, 1980{96, by Each Individual's Evaluation of the National Economy 0.6 0.8 • 0.4 • ••• •• 0.2 legislative cutpoint 0.4 0.6 • • ••• • • • • • • •• •• •••••••• •• ••• • •• • • • •• ••••••• ••• •••••••• ••••••••• • •••••••••••••••••• ••• •• • •••• • • • ••••••••••••••• •••••••••••••••••••••••••• •••••••••••••••••••••••• •• • • •••••••••••• • • • • • •••••••••••••••••••••••••••••••••••• ••••••••••••••••••••••••••••• ••••••••••• •• •••••• •••••••••••••••••••••••••••••••••• ••••••••••••••••••••••••••••••••••••• •• • •• • • •• •• • ••• ••••••••••••••••••• •••• ••••••••••••••••• ••••••••••••••••• •• •••• • •• • •• • • • • •• • • • •• • • •• ••••• •• •• •• ••• • •• •• •••••• • •• •• • •• • • • •• • • • • ••••• ••••••• ••••••• ••••••••••••••• • • • • • • • •••••••••••••••••••••••• ••••• ••••• •••••••••••••••••• ••••••••••••••••••••••••••••••••• •••••••• •••••••••• •••• •• • •••••••••••••••• • • • • ••••••• ••••••• •••••••••• •••••••••••••• •••••••••• •••• •• 0.0 • 0.0 0.2 legislative cutpoint 0.8 1.0 worse 1.0 much worse 0.0 0.2 0.4 0.6 0.8 1.0 0.0 presidential cutpoint 0.2 0.4 0.6 0.8 1.0 presidential cutpoint 0.4 0.6 •• •• • •••••••••••• ••••••••••••••••••• • • • • • ••• •••••••••••••••• •••••••••••••••••••••• ••••••••••••••• •• ••••• ••• •••••••• •••• • • • •• •• • • • ••••• •••••••• ••••••••••••••• •••••••••••• ••••••••• • • 0.2 legislative cutpoint 0.8 1.0 same • 0.0 • 0.0 0.2 0.4 0.6 0.8 1.0 presidential cutpoint 0.8 0.4 0.6 • 0.2 • • • •••••• ••• • •••••••••• • ••••••••••• • ••••••••••••••••••••••••• ••• • •••••••••••• •••••••••••••••••••• •• ••• • •• •• 0.0 0.2 ••• legislative cutpoint 0.4 0.6 • • • •• • • •••• • •• •••••••••••••••••••• ••••••••••••••••••••••••••• • • • •••••••••••••••• ••••• ••••••••••••••••••••••••••••••••••••• • • ••••••••••••••••••••••••• ••••••••••••••••••••••••••••••••••••••••• • ••••••• •••••••••• •••••••••••••• • • • • • • ••••••• •• • • • • • •• ••• 0.0 legislative cutpoint 0.8 1.0 much better 1.0 better 0.0 0.2 0.4 0.6 0.8 presidential cutpoint 1.0 0.0 0.2 0.4 0.6 0.8 presidential cutpoint 1.0 0.6 0.8 0.4 θ̂ 0.6 0.8 θ̂ 0.4 0.6 0.8 1.0 0.0 0.2 0.4 θ̂ 0.6 0.8 Independent Independent θ̂ 0.6 0.8 θ̃ 0.0 0.6 0.4 1.0 0.0 0.2 0.4 θ̂ 0.6 0.8 Republican Republican 0.0 θ̂ 0.6 0.8 θ̃ 0.0 0.6 0.4 1.0 0.0 0.2 0.4 θ̂ 0.6 0.8 Strong Republican Strong Republican 0.0 θ̂ 0.6 0.8 1.0 straight Republican ticket, Republican president, Democratic House, θ̃ 0.0 0.6 0.4 1.0 0.6 individual’s bliss point probability individual’s bliss point 0.2 1.0 0.6 individual’s bliss point probability individual’s bliss point 0.2 1.0 0.6 individual’s bliss point probability individual’s bliss point 0.2 1.0 0.6 θ̃ 0.0 probability 0.6 0.2 individual’s bliss point Legend: 0.2 Democrat θ̃ 0.0 0.0 Democrat θ̃ 0.0 0.6 1.0 individual’s bliss point θ̃ 0.0 θ̃ 0.0 probability 0.6 θ̂ 0.4 individual’s bliss point 0.0 probability 0.2 0.0 probability Strong Democrat θ̃ 0.0 probability Democratic President Strong Democrat θ̃ 0.0 probability Republican President 0.0 probability Figure 4: Vote Choice Probabilities for \Much Worse" Economy, Open Seat 0.0 0.2 0.4 θ̂ 0.6 0.8 1.0 individual’s bliss point Democratic president, Republican House, straight Democratic ticket. 0.6 0.8 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.6 1.0 0.0 0.2 0.4 0.6 0.8 Independent Independent 0.6 0.8 θ̃ θ̂ 0.0 0.6 0.4 1.0 0.0 0.2 0.4 0.6 0.8 Republican Republican 0.6 0.8 0.0 θ̃ θ̂ 0.0 0.6 0.4 1.0 0.0 0.2 0.4 0.6 0.8 Strong Republican Strong Republican 0.6 0.8 1.0 0.0 straight Republican ticket, Republican president, Democratic House, θ̃ θ̂ 0.0 0.6 0.4 1.0 0.6 individual’s bliss point probability individual’s bliss point 0.2 1.0 0.6 individual’s bliss point probability individual’s bliss point 0.2 1.0 0.6 individual’s bliss point probability individual’s bliss point 0.2 1.0 θ̃ θ̂ 0.0 0.6 probability Democrat individual’s bliss point Legend: 0.2 Democrat θ̃ θ̂ 0.0 0.0 individual’s bliss point θ̃ θ̂ 0.0 0.6 1.0 θ̃ θ̂ 0.0 θ̃ θ̂ 0.0 probability 0.6 0.4 individual’s bliss point 0.0 probability 0.2 0.0 probability Strong Democrat θ̃ θ̂ 0.0 probability Democratic President Strong Democrat θ̃ θ̂ 0.0 probability Republican President 0.0 probability Figure 5: Vote Choice Probabilities for \Much Better" Economy, Open Seat 0.0 0.2 0.4 0.6 0.8 1.0 individual’s bliss point Democratic president, Republican House, straight Democratic ticket. Strong Democrat 0.8 1.0 0.2 0.4 0.6 0.8 0.4 0.6 0.8 -0.10 probability 0.2 1.0 0.0 0.2 0.4 0.6 0.8 Independent Independent 0.6 0.8 -0.10 probability 0.4 1.0 0.0 0.2 0.4 0.6 0.8 individual’s bliss point Republican Republican 0.6 0.8 -0.10 probability -0.10 0.4 1.0 0.0 0.2 0.4 0.6 0.8 individual’s bliss point Strong Republican Strong Republican 0.6 0.8 1.0 straight Republican ticket, Republican president, Democratic House, -0.10 probability 0.4 individual’s bliss point 1.0 0.10 individual’s bliss point 0.2 1.0 0.10 individual’s bliss point 0.2 1.0 0.10 individual’s bliss point 0.10 individual’s bliss point 0.2 1.0 0.10 Democrat 0.10 Democrat -0.10 0.0 Legend: 0.0 individual’s bliss point 0.10 0.0 -0.10 probability 0.6 0.10 0.0 probability 0.4 individual’s bliss point -0.10 probability 0.0 probability 0.2 -0.10 probability 0.0 0.10 Better Republican President Strong Democrat 0.10 Better Democratic President -0.10 probability Figure 6: Dierences in Vote Choice Probabilities, Open Seat 0.0 0.2 0.4 0.6 0.8 1.0 individual’s bliss point Democratic president, Republican House, straight Democratic ticket.