This section explores the major motivations behind the new declared-strategy voting paradigm in detail. Three ideas motivate declared-strategy voting: the possibility of taking advantage of electronic voting systems to achieve more beneficial methods of vote aggregation than are feasible with traditional systems, the desire to find an information-neutral voting system, and the desire to maximize a voting system's expressiveness.
With the advent of accessible and affordable high-speed computers and interconnection networks, elections and surveys are starting to move from the voting booth, postal mail, and telephone into the computer. Voting over computer networks is likely to appeal to geographically distributed organizations such as professional societies. Existing methods of conducting surveys and elections electronically are focused on emulating (to the greatest extent possible) the feel, look, and mechanics of traditional surveys and elections, while taking advantage of the speed, accuracy, and computational power offered by the electronic system. Such approaches are quite reasonably founded on placing the computer and its associated technology in the background, so that participants suffer little shock in moving to electronic means of expressing choice. These methods thus improve on traditional voting systems, by allowing voters to cast secret ballots without being physically present at an official polling place and by introducing new ways to verify the accuracy of the election results [79]. However, these systems do nothing to improve the vote aggregation procedure itself.
A goal of this research has been to explore a new method of expressing choice that is only now made feasible by advances in computing and communications technology. Rather than simply transferring extant paradigms to the computer, this dissertation investigates the possibility of using computers to conduct surveys and elections in more beneficial and meaningful ways.
Voting theorists have long been aware that it is not always in the best interest of voters to vote for their most sincerely preferred candidates. Voting schemes in which voters can obtain a more preferred outcome by voting strategically rather than sincerely are dubbed manipulable. And it has been well established that most voting schemes used in elections with three or more alternatives (including all reasonably ``attractive'' voting schemes previously investigated) are manipulable [7, 52, 54, 94]. On the other hand, there are well-known systems that rely on randomness to elicit sincere voting behavior [7]; however, the arbitrariness present in such systems renders them generally unacceptable to voting populations.
Studies have shown empirical evidence that voting systems are manipulated by voters in real elections. Brams and Merrill [20] analyzed data collected in the 1992 National Election Study and estimated that 34.5% of Perot supporters did not vote sincerely in the 1992 Presidential election because they felt they could make better use of their votes by voting for their second-choice candidates. Cain [24] developed a model of strategic voting in the British electorate that suggests strategic manipulation does occur, especially when voters want to avoid ``wasting'' their votes or when the race is only close between two of the parties in a three party election. And Black [14] analyzed data from the 1968 and 1972 Canadian Federal elections and estimated that 12% of the voters in these elections voted for their second-choice party. It is difficult to determine how many of the voters participating in the analyzed elections voted sincerely even though they could have benefited from voting strategically. And it is uncertain whether these sincere voters voted sincerely out of ignorance of the preferences of others, ignorance of how to use preference information to their best advantage, a desire to show support for an underdog candidate, or a belief that insincere voting is dishonest.
Indeed, early criticism of manipulable voting systems equated
manipulation with dishonesty. The eighteenth century mathematician
Jean-Charles de Borda is said to have responded to criticism that his
Borda count voting scheme was manipulable by saying, ``My scheme is
only intended for honest men'' [13]. But later
theoreticians dismissed Borda's assumption that people are honor-bound
to vote for their most preferred candidate. In an introduction to
approval voting published in 1983, Brams and Fishburn wrote, ``If some
voters can do better by strategically voting for candidates other than
those they most prefer, then, instead of accusing them of dishonesty
in making rational strategy choices, it seems better to try to design
systems that make dishonesty unnecessary or costly in order for voters
to achieve their aim of electing desired candidates'' [17].
Earlier, in an 1876 pamphlet
written well before the
development of game theory, C. L. Dodgson had suggested that an
election be thought of ``more as a game of skill than a real test of
the wishes of the electors.'' He proposed that ``as my own opinion is
that it is better for elections to be decided according to the wish of
the majority than of those who happen to have most skill in the game,
I think it desirable that all should know the rule by which this game
may be won.'' Although Dodgson elaborated on the rules for winning
certain types of games, little additional work was done in this area
until 1953 when Farquharson set out to apply game theory to voting
procedures [44].
Farquharson began by introducing the concept of a voting strategy. Farquharson described a voting strategy as a plan made prior to an election that prescribes the course of action a voter should take given any contingency that can arise. In a single round election, a strategy is simply the voter's plan for how to cast a single ballot. However, in a multiple round election such as one that involves choosing between two alternatives at a time, a strategy must include a plan for all pairs of alternatives that could possibly be presented. Farquharson also discussed sincere voting, in which voters always vote for their most preferred alternatives, and sophisticated voting in which voters select utility maximizing strategies that take into account the strategies of the other voters [44].
The terms sincere, strategic, and sophisticated voting have varying definitions in the literature. Throughout this text we use the following definitions.
The application of game theory to voting theory brought on a variety of new approaches to studying voting schemes and voter behavior. It led to further investigation of the conditions under which voting schemes might be immune to manipulation, and it led to the development of models designed to provide rational choice explanations for voter behavior.
Several voting theorists, including Farquharson and Dummett [41], conjectured that it would be impossible to find a voting scheme immune to manipulation. Indeed, in the early 1970s, Gibbard and Satterthwaite independently proved that all nondictatorial voting schemes that have at least three possible outcomes, that lead to a single choice, and that do not rely on chance, are manipulable [54, 94]. Gibbard also demonstrated by example the existence of a ``mixed decision scheme'' that is neither manipulable nor dictatorial, and can allow more than two outcomes. In this scheme each voter submits a ballot containing a vote for a single alternative. One ballot is then selected at random, and the alternative specified in that ballot is declared the winner. This scheme is unsuitable for most purposes because it relies heavily on chance. Gibbard suggested that further work be done to explore decision schemes that do not leave ``too much to chance.'' This suggestion was taken up by Barbera [7], who showed that ``the only selection methods that can be both nondictatorial and nonmanipulable are those in which chance plays an extensive role.'' Gardenfors [52] also extended the work of Gibbard and Satterthwaite, focusing on voting schemes that do not necessarily select a single outcome. He showed that most of these schemes are manipulable, and those which are not tend to be very indecisive.
While these theorists were exploring the extent to which voting schemes are manipulable, other voting theorists sought to determine the optimal strategies for voters to use. McKelvey and Ordeshook developed ``A General Theory of the Calculus of Voting'' in which they derived decision rules that could be used by voters to determine their optimal strategies [69]. This article extended ``A Theory of the Calculus of Voting'' in which Riker and Ordeshook derived decision rules that could be used to determine whether it was rational for a particular voter to vote at all [87]. The theory was further generalized by Hoffman in ``A Model For Strategic Voting'' [55].
All of the decision models cited here are expected-utility models that require voters to consider their personal preferences as well as the probable preferences of the rest of the electorate. Information about the preferences of others allows voters to determine the relative probability of each candidate winning the election. When voters are able to determine such probabilities, they are said to be making decisions under risk. Without information about the preferences of others, voters are not able to determine the probabilities of the various contingencies. Merrill showed that when this occurs the sincere strategy is always the optimal strategy in plurality, Borda, and approval voting elections [70]. This is likely the case for other voting schemes as well. Merrill's results suggest that voters are only able to manipulate voting systems when they are making decisions under risk: that is, when they know the probability distribution for the various election outcomes. When voters have no information about the preferences of others they cannot manipulate the voting system.
Others have also pointed out that the fact that a voting system is manipulable does not imply that it will actually be manipulated. As Gibbard explained:
...to call a voting scheme manipulable is not to say that, given the actual circumstances, someone really is in a position to manipulate it. It is merely to say that, given some possible circumstances, someone could manipulate it [54].We assert that the circumstances required for manipulation are:
In an election where the required circumstances for manipulation are present, not all voters who could benefit from voting strategically will have sufficient knowledge and information to formulate a utility maximizing strategy. As we have discussed, the ability to manipulate is dependent on the individual voter's ability to gather information about the preferences of the other voters, but there may be costs associated with gathering this information [14]. Depending on the type of election, money, education, access to media, time, and political alliances may be necessary resources for gaining sufficiently accurate voter preference information. Because of the difficulty some voters may have in obtaining this information, it is conceivable that voters might accept inaccurate estimates -- perhaps propagated by certain candidates or their supporters -- as the truth. Indeed, it has been reported that supporters of Pat Buchanan actively sought out poll takers during the 1992 and 1996 Republican Presidential primaries so that pre-election polls would show more support for Buchanan than actually existed [26]. In addition, as noted by Black [14], some voters ``may hold probability estimates that are inflated or clearly erroneous or the product of the simple mimicking of the views of a close friend or spouse.'' Moreover, the ways that poll data and other preference information flow through society and are interpreted by voters are not well understood [16].
Thus, we conclude that a significant problem with manipulable voting systems is that they allow voters with more accurate information about the preferences of others to use their votes more effectively than other voters, essentially granting these voters a weighted vote. This is contrary to the principles espoused by many democratic countries and organizations in which all people are given the same amount of say in the electoral process, regardless of their means. Those who subscribe to these principles often expect that by granting each individual one vote, they are granting all people equal voting power. However, this is not necessarily the case when some voters have the means to obtain information about the preferences of other voters that is unavailable to everyone. These voters may use this information to formulate optimal voting strategies which cannot be identified in the absence of such information.
Another problem with manipulable voting systems is that not all voters understand the formulation of utility-maximizing functions. Thus, even if all voters have equal information about the preferences of others, those who understand the formulation procedure have more power than those who do not. Riker [86] notes that when strategic voting occurs frequently, the meaning of social choices ``may consist simply of the tastes of some people (whether majority or not) who are skillful or lucky manipulators.''
A goal of this research has been to design a voting system that approaches information neutrality: that is, a system in which all voters will have equal access to both the information and knowledge needed to vote strategically.
Manipulable voting systems frustrate attempts at analyzing and interpreting election results because analysts cannot distinguish between voters who voted sincerely and those who voted insincerely. Thus, election results give little indication as to whether a winning alternative had strong support from those who voted for that alternative. As noted by Knight and Johnson [62], ``Social choice theorists demonstrate that any electoral outcome is at least partly an artifact of the aggregation mechanism through which it is produced. Therefore, electoral results always require interpretation and justification.'' Insincere voters add a degree of uncertainty to such interpretation.
In addition, voters correctly view elections as opportunities to voice their opinions to their government. They may resent the fact that in order to get the most value from their vote (voting strategically) they in effect lose their opportunity to make their true opinions known. These voters basically have to choose between casting an effective or an expressive vote.
Brams and Fishburn [17] suggest that if voting systems allowed voters better opportunities to express their preferences, more people would be likely to vote:
Voters who think they might be wasting their votes, or who cannot decide which of several candidates best reflects their views, would not be on the horns of a dilemma. By not being forced to make a single -- perhaps arbitrary -- choice, they would feel that the election system allows them to be more honest. We believe this would make voting more meaningful and encourage greater participation in elections.
Thus, a goal of this research has been to develop a voting system that will allow voters to vote effectively while still expressing their opinions. Such a system would give voters the satisfaction of expressing themselves and analysts the sincere data with which to interpret election results.