Home The Impact of Voter Uncertainty and Alienation on Turnout and Candidate Policy Choice
Article
Licensed
Unlicensed Requires Authentication

The Impact of Voter Uncertainty and Alienation on Turnout and Candidate Policy Choice

  • Natalya R. Brown EMAIL logo
Published/Copyright: July 1, 2014
The B.E. Journal of Theoretical Economics
From the journal The B.E. Journal of Theoretical Economics Volume 14 Issue 1

Abstract

Formal models of elections typically assume that voters are sure of their ideal points on the policy spectrum. Meanwhile, the empirical evidence suggests that voters are often uncertain about their ideal positions. In addition, alienation appears to play a key role in explaining voter turnout in elections. Using a spatial model that incorporates abstentions and the concepts of alienation and tolerance, I show that a positive correlation between extreme policy preferences and certainty among voters can affect voter turnout and result in the divergence of candidate policy choices.

Keywords: elections; voter uncertainty; voter turnout; alienation

Appendix: Proofs

PROPOSITION 1: (xL∗,xR∗)=(θ−1,1−θ)is the unique Nash equilibrium of the election game. In addition, xL∗=θ−1is the unique weakly dominant strategy for candidate L, andxR∗=1−θis the unique weakly dominant strategy for candidate R.

PROOF: First, the best response policy position for candidate R, given the policy position of candidate L must be determined. Suppose that xL∈XL and 0≤xR<1−θ, so that the upper limit of the segment representing candidate R’s voting bloc, μˉR=λR2<1. In addition, suppose that λR1>xL+xR2, so that the lower limit of the segment of voters that would vote for candidate R, μ_R=λR1. Then, the size of candidate R’s voting bloc is

s(BR|xL,xR)=4υmxR2+4(1−υm)(θ−υm)1−υm

which is strictly increasing in xR. However, if λR1<xL+xR2, so that μ_R=xL+xR2, then the size of candidate R’s voting bloc is

s(BR|xL,xR)=xR(1+υm)2(1−υm)+υmxR21−υm2+θ−υm1−υm−xL2

which is also strictly increasing in xR. So for xL∈XL, when 0≤xR<1−θ, s(BR|xL,xR) is strictly increasing in xR.

Now suppose that xL∈XL and 1−θ<xR≤1, so that the upper limit of the segment representing candidate R’s voting bloc is equal to 1. In addition, suppose that, λR1>xL+xR2, so that the lower limit of the segment of voters that would vote for candidate R, μ_R=λR1. Then, the size of candidate R’s voting bloc is

s(BR|xL,xR)=1−xR1−υm+υmxR21−υm2+θ−υm1−υm

which is strictly decreasing in xR. However, if λR1<xL+xR2, so that μ_R=xL+xR2, then the size of candidate R’s voting bloc is

s(BR|xL,xR)=1−xL+xR2

which is also strictly decreasing in xR. So for xL∈XL, when 1−θ<xR≤1, s(BR|xL,xR) is strictly decreasing in xR. Therefore, for any xL∈XL, xR∗=1−θ maximizes the size of candidate R’s voting bloc.

Similarly, s(BL|xL,xR) is strictly decreasing in xL, when θ−1<xL≤0 and strictly increasing in xL when −1≤xL<θ−1. Therefore, for any xR∈XR, xL∗=θ−1 maximizes the size of candidate L’s voting bloc. Recall that xR1(xL)≤xR2(xL) are the two values of xR∈XR such that s(BL|xL,xR)=s(BR|xL,xR). xR1(xL) and xR2(xL) are defined in eqs [17] and [18].

The best response correspondence for candidate R given the policy position of candidate L is therefore,

xR*(xL)={(xR1(xL),xR2(xL))ifxL∈(θ−1,0]|xL|ifxL=θ−1(xR1(xL),xR2(xL))ifxL∈[−1,θ−1)

Note that 1−θ∈xR1(xL),xR2(xL). The best response correspondence for candidate L given the policy position of candidate R is analogous.

xL*(xR)={(xL1(xR),xL2(xR))ifxR∈[0,1−θ)−xRifxL=1−θ(xL1(xR),xL2(xR))ifxR∈(1−θ,1]

Also, θ−1∈xL1(xR),xL2(xR). Finally,

πR(xL,1−θ)={1/2if xL=θ−11otherwiseand
πL(θ−1,xR)={1/2if xR=1−θ1otherwise  ∎

PROPOSITION 2: If1+υm>2θ, there exists a segment of voters (in the middle) who will abstain. The size of the segment of voters who abstain iss(A)=21+υm−2θ1−υm.

PROOF: Now, λR1=xR∗1−υm−υmxR∗21−υm2+θ−υm1−υm and λL2=−xR∗1−υm+υmxR∗21−υm2+θ−υm1−υm, where xR∗=1−θ. If there is a segment of voters in the middle who will abstain, this implies that μ_R≠0 and μˉL≠0 (i.e. λR1>0>λL2). So the size of the segment of voters who abstain is s(A)=λR1−λL2=2(xR*1−υm−υmxR*2(1−υm)2+θ−υm1−υm)=2[1+υm−2θ1−υm]>0 if 1+υm>2θ∎

References

Abramowitz, A. I. 2010. The Disappearing Center: Engaged Citizens, Polarization, and American Democracy. New Haven, CT: Yale University Press.Search in Google Scholar

Adams, J., B.Bishin, and J.Dow. 2004. “Representation in Congressional Campaigns: Evidence for Directional/Discounting Motivation in United States Elections.” Journal of Politics62(2):348–73.10.1111/j.1468-2508.2004.00155.xSearch in Google Scholar

Adams, J., J.Dow, and S.Merrill III. 2006. “The Political Consequences of Alienation-Based and Indifference-Based Voter Abstention: Applications to Presidential Elections.” Political Behavior28(1):65–86.10.1007/s11109-005-9002-1Search in Google Scholar

Adams, J., and S.Merrill III. 2003. “Voter Turnout and Candidate Strategies in American Elections.” The Journal of Politics65(1):161–89.10.1111/1468-2508.t01-1-00008Search in Google Scholar

Alesina, A., and H.Rosenthal. 1995. Partisan Politics, Divided Government, and the Economy. New York: Cambridge University Press.10.1017/CBO9780511720512Search in Google Scholar

Alesina, A., and H.Rosenthal. 1996. “A Theory of Divided Government.” Econometrica64:1311–43.10.2307/2171833Search in Google Scholar

Alvarez, R. M. 1998. Information and Elections. Revised to Include the 1996 Presidential Elections. Ann Arbor: University of Michigan Press.Search in Google Scholar

Ansolabehere, S., and J. M.Snyder Jr. 2000. “Valence Politics and Equilibrium in Spatial Election Models.” Public Choice103:327–36.10.1023/A:1005020606153Search in Google Scholar

Aragones, E., and Z.Neeman. 2000. “Strategic Ambiguity in Electoral Competition.” Journal of Theoretical Politics12(2):183–204.10.1177/0951692800012002003Search in Google Scholar

Berger, M. M., M. C.Munger, and R. F.Potthoff. 2000. “With Uncertainty, the Downsian Model Predicts Divergence.” Journal of Theoretical Politics12:228–40.10.1177/0951692800012002005Search in Google Scholar

Blais, A., and D.Rubenson. 2013. “The Source of Turnout Decline: New Values or New Contexts.” Comparative Political Studies46(1):95–117.10.1177/0010414012453032Search in Google Scholar

Blomberg, S. B., and J. E.Harrington Jr. 2000. “A Theory of Rigid Extremists and Flexible Moderates with an Application to the U.S. Congress.” American Economic Review90(3):605–20.10.1257/aer.90.3.605Search in Google Scholar

Calvert, R. 1985. “Robustness of the Multidimensional Voting Model: Candidate Motivations, Uncertainty, and Convergency.” American Journal of Political Science29:69–95.10.2307/2111212Search in Google Scholar

Carmines, E. G., M. J.Ensley, and M. W.Wagner. 2012. “Who Fits the Left-Right Divide? Partisan Polarization in the American Electorate.” American Behavioral Scientist56:1631–53.10.1177/0002764212463353Search in Google Scholar

Davis, O. A., M. J.Hinich, and P. C.Ordeshook. 1970. “An Expository Development of a Mathematical Model of the Electoral Process.” American Political Science Review64(2):426–48.10.2307/1953842Search in Google Scholar

Downs, A. 1957. An Economic Theory of Democracy. New York: Harper and Row.Search in Google Scholar

Enelow, J. M., and M. J.Hinich. 1984. The Spatial Theory of Voting. New York: Cambridge University Press.Search in Google Scholar

Erikson, R., and G.Wright. 1992. “Voters, Candidates, and Issues in Congressional Elections.” In Congress Reconsidered, 6th ed., edited by L.Dobb and B.Oppenheimer. Washington, DC: Congressional Quarterly Press.Search in Google Scholar

Erikson, R., and G.Wright. 2000. “Representation of Constituency Ideology in Congress.” In Continuity and Change in House Elections, edited by D.Brady, J.Cogan, and M.Fiorina. Stanford, CA: Stanford University Press.10.1515/9780804764377-011Search in Google Scholar

Faulí-Oller, R., E. A.Ok, and I.Ortuño-Ortín. 2003. “Delegation and Polarization of Platforms in Political Competition.” Economic Theory22:289–309.10.1007/s00199-002-0305-8Search in Google Scholar

Fernbach, P. M., T.Rogers, and C. R.Fox. 2013. “Political Extremism Is Supported by an Illusion of Understanding.” Psychological Science24(6):939–46.10.1177/0956797612464058Search in Google Scholar

Fiorina, M. P. 2002. “Parties, Participation, and Representation.” In Political Science: The State of the Discipline, edited by T.Katznelson and H.Milnes, 537–38. New York: Norton.Search in Google Scholar

Fiorina, M. P., S. J.Abrams, and J. C.Pope. 2011. Culture War? The Myth of a Polarized America, 3rd ed. New York: Pearson-Longman.Search in Google Scholar

Fleck, R. K. 1999. “The Value of the Vote: A Model and Test of the Effects of Turnout on Distributive Policy.” Economic Inquiry37(4):609–23.10.1111/j.1465-7295.1999.tb01451.xSearch in Google Scholar

Glaeser, E. L., G. A.Ponzetto, and J. M.Shapiro. 2005. “Strategic Extremism: Why Republicans and Democrats Divide on Religious Values.” Quarterly Journal of Economics120(4):1283–330.10.1162/003355305775097533Search in Google Scholar

Hetherington, M. J. 2008. “Turned Off or Turned on? How Polarization Affects Political Engagement.” In Red and Blue Nation? Consequences and Correction of America’s Polarized Politics, edited by P. S.Nivolo and D.W.Brady. Washington, DC: Brookings.Search in Google Scholar

Hetherington, M. J. 2009. “Putting Polarization in Perspective.” British Journal of Political Science39:413–48.10.1017/S0007123408000501Search in Google Scholar

Hill, K. Q., J. E.Leighley, and A.Hinton-Andersson. 1995. “Lower-Class Mobilization and Policy Linkage in the U.S. States.” American Journal of Political Science39(1):75–86.10.2307/2111758Search in Google Scholar

Hinich, M. J. 1977. “Equilibrium Spacial Voting: The Median Voter Result Is an Artifact.” Journal of Economic Theory16:208–19.10.1016/0022-0531(77)90005-9Search in Google Scholar

Hinich, M. J., and P. C.Ordeshook. 1969. “Abstentions and Equilibrium in the Electoral Process.” Public Choice7:81–106.10.1007/BF01718735Search in Google Scholar

Layman, G. C., and T. M.Carsey. 2002. “Party Polarization and ‘Conflict Extension’ in the American Electorate.” American Journal of Political Science46:786–800.10.2307/3088434Search in Google Scholar

Lee, D. S., E.Moretti, and M. J.Butler. 2004. “Do Voters Effect or Elect Policies? Evidence from the US House.” Quarterly Journal of Economics119(3):807–59.10.1162/0033553041502153Search in Google Scholar

Lewin, K., T.Dembo, L.Festinger, and P. S.Sears. 1944. “Level of Aspiration.” In Personality and the Behaviour Disorders, Vol. I, edited by J. M. Hunt, 333–78. New York: Ronald.Search in Google Scholar

McCarty, N., Poole, K.T. and H.Rosenthal. 2006. Polarization America: The Dance of Ideology and Unequal Riches. Cambridge, Massachusetts: MIT Press.Search in Google Scholar

Nownes, A. J. 1992. “Primaries, General Elections, and Voter Turnout: Multinomial Logit Model of the Decision to Vote.” American Politics Quarterly20:205–27.10.1177/1532673X9202000204Search in Google Scholar

Poole, K. T., and H.Rosenthal. 1984. “The Polarization of American Politics.” Journal of Politics46:1061–79.10.2307/2131242Search in Google Scholar

Rogowski, J.C. 2014. “Electoral Choice, Ideological Conflict, and Political Participation.” American Journal of Political Science58(2):479–494.10.1111/ajps.12059Search in Google Scholar

Schkade, D., C. R.Sunstein, and R.Hastie. 2010. “When Deliberation Produces Extremism.” Critical Review22(2–3):227–52.10.1080/08913811.2010.508634Search in Google Scholar

Siegel, S. 1957. “Level of Aspiration and Decision Making.” Psychology Review64(4):253–62.10.1037/h0049247Search in Google Scholar

Simon, H. A. 1959. “Theories of Decision-Making in Economics and Behavioral Science.” The American Economic Review49(3):253–83.Search in Google Scholar

Snyder, J. 1994. “Safe Seats, Marginal Seats, and Party Platforms: The Logic of Party Differentiation.” Economics and Politics6(3):201–13.10.1111/j.1468-0343.1994.tb00097.xSearch in Google Scholar

Teixeira, R. 1987. Why Americans Don’t Vote: Turnout Decline in the United States 1960–1984. New York: Greenwood Press.Search in Google Scholar

Teixeira, R. 1992. The Disappearing Voter. Washington, DC: Brookings Institution.Search in Google Scholar

Wittman, D. A. 1983. “Candidate Motivation: A Synthesis of Alternatives.” American Political Science Review77:142–57.10.2307/1956016Search in Google Scholar

  1. 1

    For example, voter turnout in presidential elections declined between 1960 and 2000, rebounding between 2004 and 2012.

  2. 2
  3. 3

    Enelow and Hinich (1984), and Calvert (1985) provide reviews of earlier extensions of the standard model incorporating measures such as uncertainty over the candidates’ policy positions or candidate motivations.

  4. 4
  5. 5

    In addition to those on page 7.

  6. 6

    Suppose that all voters have the same υi regardless of the location of their preferred policies, or there is no uncertainty, that is υi=0. Then the multiple equilibria is characterized by xL∗∈2θ−1,0 and xR∗∈0,1−2θ.

  7. 7

    This would be equivalent to θxi becoming steeper.

  8. 8

    The divergence result requires that the loss of moderate voters is initially outweighed by the gains of less voters. That is, the marginal increase in the confidence of voters as we move away from the center initially outweighs the decline in the probability distribution. Specifically, gμˉcΔμˉc−gμ_cΔμ_cΔxc is initially positive as xc moves away from 0.

  9. 9
  10. 10
Published Online: 2014-7-1
Published in Print: 2014-1-1

©2014 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Contributions
  3. Cheap Talk and Editorial Control
  4. Adverse Effects of Patent Pooling on Product Development and Commercialization
  5. Discretionary Acquisition of Firm-Specific Human Capital under Non-verifiable Performance
  6. On-the-Job Search and Finding a Good Job Through Social Contacts
  7. Replication and Returns to Scale in Production
  8. An Adaptive Learning Model with Foregone Payoff Information
  9. A Single Parent’s Labor Supply: Evaluating Different Child Care Fees within an Intertemporal Framework
  10. Dynamic Price Discrimination with Customer Recognition
  11. Cournot and Bertrand Competition in a Model of Spatial Price Discrimination with Differentiated Products
  12. The Impact of Voter Uncertainty and Alienation on Turnout and Candidate Policy Choice
  13. Topics
  14. Trust, Truth, Status and Identity: An Experimental Inquiry
  15. Macro Meets Micro: Stochastic (Calvo) Revisions in Games
  16. The Robustness Case for Proportional Liability
  17. The Rise and Spread of Favoritism Practices
  18. Moral Hazard and Tradeable Pollution Emission Permits
  19. Reciprocity in the Principal–Multiple Agent Model
https://doi.org/10.1515/bejte-2013-0007
Keywords for this article
elections; voter uncertainty; voter turnout; alienation

Articles in the same Issue

  1. Frontmatter
  2. Contributions
  3. Cheap Talk and Editorial Control
  4. Adverse Effects of Patent Pooling on Product Development and Commercialization
  5. Discretionary Acquisition of Firm-Specific Human Capital under Non-verifiable Performance
  6. On-the-Job Search and Finding a Good Job Through Social Contacts
  7. Replication and Returns to Scale in Production
  8. An Adaptive Learning Model with Foregone Payoff Information
  9. A Single Parent’s Labor Supply: Evaluating Different Child Care Fees within an Intertemporal Framework
  10. Dynamic Price Discrimination with Customer Recognition
  11. Cournot and Bertrand Competition in a Model of Spatial Price Discrimination with Differentiated Products
  12. The Impact of Voter Uncertainty and Alienation on Turnout and Candidate Policy Choice
  13. Topics
  14. Trust, Truth, Status and Identity: An Experimental Inquiry
  15. Macro Meets Micro: Stochastic (Calvo) Revisions in Games
  16. The Robustness Case for Proportional Liability
  17. The Rise and Spread of Favoritism Practices
  18. Moral Hazard and Tradeable Pollution Emission Permits
  19. Reciprocity in the Principal–Multiple Agent Model
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 12.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/bejte-2013-0007/html
Scroll to top button