Difficulties in expressing voters` true preferences

Who governs democracy?

Term Paper (Advanced seminar), 2006

27 Pages, Grade: 1,7



1 Introduction

2 Strategic Voting as intended falsification of voters` true preferences
2.1 A critique on Lijphart`s disproportionality measure
2.2 Incentives for Strategic Voting under different Electoral Systems
2.3 How to reveal voters` true preferences
2.3.1 How to design the electoral system
2.3.2 A lack of information for more sincere voting?
2.4 Conclusion

3 Media as Instrument for shaping voters` expressed preferences
3.1 Why voters cannot express their true preferences
3.1.1 Hume`s Problem of Induction
3.1.2 The paradox of voting
3.2 How Media shapes voters` expressed preferences
3.2.1 Why there is collusion
3.2.2 Shaping voters` expressed preferences The Creation of mutual beliefs Persuasion
3.3 Whose and What kind of preferences are expressed?

4 Conclusion

5 References

1 Introduction

This paper shows that it is quite unlikely that voters are able express their true preferences sufficiently.

In the first part I assume a voter who is aware of his own true preferences. However, the electoral system offers an incentive to vote strategically. In such a situation the voter is aware that he doesn`t express what he favours most, but what he thinks he can support without wasting his vote. I will show that it is possible to limit the incentive for voting strategically either by the choice of the electoral system or by the abolishment of polls.

The second part shows first that it is quite unlikely that a voter is able to identify his true preferences, either because of Hume`s problem of Induction or because of complexity. Complexity is enhanced when Media comes into the game, because voters have to consider both the argument and those who created the argument.

Therefore it is necessary to show, that Media has an incentive to collude. If one assumes Media to collude it doesn`t explain why voters` preferences are shaped. Preferences are shaped either due to media`s creation of mutual beliefs or by persuasion. Persuasion refers to complexity, because it is rather difficult to consider additionally the interests of those who created a certain media product.

However, votes are expressed and aggregated. But whose or what preferences are that?

2 Strategic Voting as intended falsification of voters` true preferences

In this part I assume that a voter knows his true preferences and that he will vote for that party having the smallest ideological distance to him on a left-right-continuum. Section 1 shows that there is an incentive for a voter not to vote according to his actual preferences, but to vote strategically. By doing so the voter views himself to be better off, because he expects either to waste his vote or to be worse off by voting truthfully. But what does the aggregate of votes represents, if a lot of voters decide to do so? This is called misrepresentation.[1] This is why I ask how to design an electoral system that guarantees that „individuals will actually express their true tastes even when they are acting rationally.“[2]

2.1 A critique on Lijphart`s disproportionality measure

According to Lijphart the electoral system is defined by „the set of methods for translating the citiziens`votes into representatives`seats“[3]. Additionally Lijphart defines disproportionality as „the deviation of parties` seat shares from their vote shares“[4]. This deviation may has many reasons, for example the existence of a threshold or the size of the district magnitue: the higher the threshold the higher disproportionality and the higher the district magnitue the lower disproportionality. Lijphart measures disproportionality with the Least Square Index:

illustration not visible in this excerpt

The share of votes for party i are denoted by vi, the share of seats for party i are denoted by si. As one can see this kind of measure implies a problem, because Lijphart doesn`t consider the emergence of one`s vote sufficently.

Disproportionality as defined by Lijphart measures two effects at the same time: the mechanical effect and the psychological effect. The mechanical effect is what Lijphart intends to measure only, namely „the deviation of parties` seat shares from their vote shares“[5]. The psychological effect is a result of the voter`s awareness of the mechanical effect: „in an electoral system based on plurality voting, it is notorious that an individual who really favors a minor party candidate will frequently vote for the less undesireable of the major party candidates rather than ‚throw away his vote`“.[6] Although Lijphart knows that there is a psychological effect that might affect the number of elective parties[7] and that by limiting the number of elective parties disproportionality tends to decrease[8], his conclusion remains unchanged: the less disproportionality the better[9]. He also recognizes an „overall direction of the changes in election rules [...] towards more proportional rules“[10].

But a lower Least Square Index does not represent an increase of proportionality. In fact, the opposite might be true. A higher mechanical effect may cause a higher psychological effect. The higher the psychological effect the lower the disproportionality measured by Lijphart. As an hypothetical example a one-party-system is the most proportional one, because of a very strong psychological effect. This is why it is necessary to consider how decisions which party to vote for are made, i.e. to focus on the psychological effect.

Because of the reasons mentioned above disproportionality cannot be the variable that allows to justify that an electoral system is somewhat superior or inferior to another or that such a development has to be judged as an improvement. Lijphart changes two aspects at the same time: the electoral system and the composition of votes. However, for the purpose of comparison, it is requiered that the composition of votes remains unchanged in order to reveal a superior or inferior electoral system concerning the transfer of votes into seats, e.g. the reduction of a threshold c.p. will lead to a superior electoral system. Whether the reduction of a threshold implies other problems is another question, but any composition of votes is more proportional transferred than before. Nevertheless this does not reveal the pure mechanical effect, because votes imply the psychological effect.

A separation of both effects is offered by Clark and Golder (2006) by the introduction of social cleavages as an ethnic group. A further ethnic group demands legislative representation, but the less permissive the electoral system the higher the psychological and the mechanical effect. Table 3 by Clark and Golder shows in support to Lijphart that countries with a low district magnitude are less permissive, but also that the demand of an additional ethnic group for legislative representation cannot be seen in votes, because of the stronger strategic (psychological) effect. An additional ethnic group in Australia for example creates an increase of elected parties of only 0,11 which is additionally reduced to 0,07 legislative parties by the pure mechanical effect.[11] Thus the psychological effect reduces the demand about 90%, i.e. voter`s decisions reduce disproportionality what the Least Square Index doesn`t reflect. This is why I focus on incentives for strategic voting in the next section.

2.2 Incentives for Strategic Voting under different Electoral Systems

I assume that the rational voter is aware of the mechanical effect and considers that information, so not to waste his vote. I secondly assume, that the voter has information about the propable decision of other voters, because of published polls. It follows that the voter, because of knowing his own preference and the other voter`s preferences has to make a decision between two alternatives: either to vote truthfully (party A) or to vote strategically (party B). The same is true for a voter on the other side of the left-right-continuum, namely to vote truthfully for party D or strategically for party C. If only one of the voters votes strategically his strategic vote is decisive and creates the winner. If both vote strategically, party B or C might be the winner. If both vote sincerely, either party A or might be the winner. Voter 1 has the preferences A>B>C>D, while voter 2 has the opposite preferences D>C>B>A. So one can create a two-player game presented in picture 1[12] where higher payoffs represent a higher utility level:

illustration not visible in this excerpt

Thus the only Nash Equilibrium in pure strategies is voting strategically for both players, namely party B and party C, independent on the assumption of the four possible election results, i.e. party A, B, C or D will win. As one can see it is rational to vote strategically, if at least one of the players assumes the other one will do so. As shown in picture 2[13] voting truthfully might only create an additional Nash Equilibrium if both players assume their preference to win, what is unlikely because both have the same information, that is published by polls.

The abstract example above fits well Plurality voting systems, that I am goint to view in more detail now. Therefore I assume the following preferential order to be the true order[14]:

31% ABCD 16% BADC 20% CBAD 33% DCBA

In plurality rule systems each voter has one vote and the party who receives the most votes is the winner. Thus party D is elected, because what counts is the first preference only.

How can someone manipulate the result? The voters having the preferential order ABCD have the strongest incentive to prevent party D to be elected. What can they do? They can insincerely vote for B instead of A, so B will receive 47% of all votes and will be elected. The argument can be repeated for those with the preferential order DCBA, thus C will receive 53% and prevail. This strategy is called compromising[15], i.e. ranking a preference higher that is not the true one in order to get it elected.

Because plurality rule counts only one (the first) preference it ignores all further preferences. Thus the incentive to vote strategically is strong, because the possibility to waste one`s vote is high. What about other voting systems, that consider more further preferences?

Similar to plurality is Approval Voting (AV), but the voter is allowed to vote for as many candidates as he likes. Each vote has the same weight, so there is no ranking possible. Either he votes for a candidate or he doesn`t. Thus Plurality and AV will create the same result, if all voters express their first preferences only. Who will prevail, if all voters express their first two preferences? B will be elected, because it received the most of all votes: 67%. How can someone manipulate the result? Those 20% of voters who voted equally for B and C, can withdraw their vote for B. Thus C is elected.

Because plurality and AV do not allow voters to rank their preferences I present Rank Order Voting, also called Borda Count in the following. Each voter assigns four points to his first preference, three to the next preference and so on. The points are added and the winner is, who has the biggest total[16]. According to this party B wins[17]. How can someone manipulate the result? Voters with the preferential order DCBA might switch their first two preferences in order to maximize the points for party C. This is enough to ensure party C to win the election[18] what is in accordance to these voter`s preferences. Another group of voters might manipulate the result in a similar way, namely those with the preferential order CBAD might switch B and D, so to lower the points for B. This is enough to ensure party C to win. But as one can see because of the close result[19] this strategy might backfire, if D receives strategically too many points.


[1] see Arrow 1951: 7 and Elster 1998: 6

[2] Arrow 1951: 7

[3] Lijphart 1994: 1

[4] Lijphart 1994: 54

[5] Lijphart 1994: 54

[6] Arrow 1951: 7

[7] Lijphart 1994: 72

[8] Lijphart 1994: 131

[9] Lijphart proposes in chapter 7 some methods aiming at reducing disproportionality. In fact these proposals are concerned with the mechanical effect only

[10] Lijphart (1994): 141

[11] Clark and Golder 2006

[12] own illustration

[13] own illustration

[14] In fact 4! = 24 possible combinations exist, however simplification doesn`t cover the argument

[15] http://condorcet.org

[16] vgl. Maskin 2005: 2

[17] A: 245 points = 25% B: 283 points = 28% C: 257 points = 26% D: 215 points = 22%

[18] A: 245 points = 25% B: 283 points = 28% C: 290 points = 29% D: 182 points = 18%

[19] A: 245 points = 25% B: 243 points = 24% C: 257 points = 26% D: 255 points = 26%

Excerpt out of 27 pages


Difficulties in expressing voters` true preferences
Who governs democracy?
University of Mannheim  (Fakultät für Sozialwissenschaften)
Europäische Demokratien im Vergleich
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ISBN (Book)
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Difficulties, Europäische, Demokratien, Vergleich
Quote paper
André Heinze (Author), 2006, Difficulties in expressing voters` true preferences, Munich, GRIN Verlag, https://www.grin.com/document/116411


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