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Question 1
Write down a model of a two-candidate electoral competition in which:
(i) candidates are ideological and (ii) there is a nash equilibrium in which the platforms chosen by each candidate are the same.
Answer:
The model of a two - candidate electoral competition in which the candidates are ideological and use the same platform of Nash equilibrium is the spatial theory of elections. A candidate’s ideological label may imply different issue positions to different users. There is a connection between the ideology and the issues in the mind of the voters and the relationship between this connection and the electoral prospects of candidates engaged in two-candidate competition is linked and each voter’s preference between two candidates is based on the estimated issue positions of the candidates. However, the connection that exists in each voters’ mind between the positions on the issues and the position on the predictive dimension induces single-peaked preferences for each voter on the predictive dimension.
Every voter has owned point on this dimension, similar to an ideal point on a single issue. A form of the median implies that if two candidates compete for votes, the candidate closest to the median most preferred point wins a majority of the votes if this point is unique.
In this model we assume that a single predictive dimension underlies electoral competition and for reasons of specificity we will assume that this dimension measures political ideology.
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We will define political ideology in more general terms than are usually employed. To understand the connection between ideology and issues in the minds of the voters and the electoral prospects of the candidates engaged in the two candidate competition, we need to seek conditions on voter’s perception that either benefit or disadvantage incumbents. The issue positions that we assume to be of concern to the voters are not positions taken by the candidate during the campaign but rather the real policies that the voter expects will prevail if the candidate is elected. This assumption is important to the competition as it is a fact that each voter bases his preference between two candidates on the degree to which he expects the real policy preferences, given the selection of one candidate than another. So It is established on the basis that the extent to which ideological differences between elected officials have been associated with differences in the actual policies that have prevailed under these officials. (Jstor.org, 2016)
Question 2
Discuss: The negative results of the Social Choice theory have had a pro- found effect on the field of Political economy.
Answer:
Social choice theory is a theoretical framework to analyze individual opinions, preferences, welfares or interests to reach a decision which is collective or social welfare in some sense. In short it is a study of collective decision processes and procedures. In the political economy which is concerned with votes, preferences, judgments, welfare the social choice theory help to create results concerning the aggregation of individual inputs. (2016)
Central questions arise is How can a group of individuals choose the winning outcome from the given options?
How can we call a voting system democratic?
How can we rank from different social alternatives in order of social welfare?
A successful society must develop structure of laws and leadership that will fulfill people’s expectations in all situations. The basic social need is the coordination between leadership and political institution which is not met by all the political parties to create a society which is corruption free and helps a country to meet its goals as a developed country. The political economy is very diverse and enormous.
Social theory gives a chance to make mathematical social science general statements about all such institutions, because of the diversity of the potential institutions the power of the social choice theory becomes limited. The limitations of the social choice theory are that whole society will be affected with the choice of the candidate and if the wrong candidate is selected whole society will have to go all over again with the time, efforts and money to select the other next candidate which is not possible in all cases. The voting system has become manipulable, corrupt and non-separable because of the wrong use of means used by some political parties all the results are not justified and legitimate.
If ‘a’ gets more votes than ‘b’ he is mentioned socially preferred but if there are three or more candidates it becomes difficult to choose the leader.
The social choice theory may seem like an attractive method but it is impossible to exclusively rely on it as all the judgments are not fair and legitimate rather sometimes manipulative, corrupt or wrong. (2016).
Question 3
In the citizen-candidate model with a winner-takes-all election, under what conditions on h (the benefit of winning) and c (the cost of running) does a two-candidate equilibrium exist in which both the candidates have an ideal point at the median?
Answer:
Citizen candidate model postulates that any citizen may become a candidate for office, that a winner is chosen from among the candidates by voting with ties broken by the flipping of a coin, that all voters have preferences among a set of policies and that the office holder adopts his set of preferred policies. It has been proven on certain assumptions that there exists an equilibrium in these models and that the equilibrium is efficient. (Usher, 2003)
Citizen candidate models break the artificial bounds in the older literature between people voting for candidates for office and legislators voting about policies, incorporating both into a model of the democratic process where voters and candidate are drawn from the same population.
The conditions on which two candidate equilibrium exists between b (the benefit of winning) and c (the cost of running) where both the candidates have an ideal point at the median:
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1) Politics is the choice out of a set of options available.
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2) Everybody has preferences over policies.
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3) Everybody is fully aware of everybody else’s preferences.
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4) Anybody may run as a candidate.
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5) The candidates may adopt whatever preferred policies. No promise to do otherwise would be believed. The selected candidate becomes an elected dictator (the winner takes it all), governing all by himself with no legislature and no political parties.
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6) In the event of a tie between the candidates the winner of the election is determined by lot. This assumption is important because ties frequently emerge in the world of citizen-candidate model.
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7) In voting and in deciding whether to run for the position, people act individually, rationally, selfishly without altruism and without deliberate cooperation.
The Nash Equilibrium as a criterion for order in the political realm.
The search for a political equilibrium can be looked upon not as a quest that must ultimately succeed or fail, but as the attempt to see how much of the political realm can be subsumed within the domain of self-interest so as to identify the minimal domain within which something more than self-interest, conscious cooperation or respect to constitutional constraints is required. (2016)
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(2016). Retrieved 27 January 2016, from http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1013.pdf
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Enelow, J., & Hinich, M. (1989). A general probabilistic spatial theory of elections. Public Choice, 61(2), 101-113. http://dx.doi.org/10.1007/bf00115657
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Introduction, T., Enelow, J., & Hinich, M. (2016). The Spatial Theory of Voting. Cambridge University Press. Retrieved 27 January 2016, from http://www.cambridge.org/us/academic/subjects/politics-international-relations/political-theory/spatial-theory-voting-introduction
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List, C. (2013). Social Choice Theory. Plato.stanford.edu. Retrieved 27 January 2016, from http://plato.stanford.edu/entries/social-choice/#MeaIntComWel
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question, N. (2016). Nash equilibrium question. Math.stackexchange.com. Retrieved 27 January 2016, from http://math.stackexchange.com/questions/73158/nash-equilibrium-question
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Usher, D. (2003). Testing the Citizen-Candidate Model. Working Papers. Retrieved from https://ideas.repec.org/p/qed/wpaper/1013.html
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(2016). Retrieved 27 January 2016, from http://www2.warwick.ac.uk/fac/soc/economics/staff/academic/dhillon/publications/jpet4.pdf
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