Introduction and Overview

Before the 1950 [UK] election the following question was asked in a Gallup poll: Would you vote Liberal if you thought the Liberals could win? To this question, no less than 38 per cent replied `yes' -- 28 per cent more than then intended to vote Liberal and 29 per cent more than actually did so. That is to say, the votes of more than one-quarter of the entire electorate were determined less by what they themselves wanted than by what they guessed most of the other electors to want. Knowing that this was so, the larger parties ...devoted much of their efforts to the capture of potential Liberal voters, not by extolling their own virtues or by attacking any feature of the Liberal programme, but by persuading the electors that the Liberal candidates had no chance -- `a vote for the Liberal is a vote wasted'.

Enid Lakeman, 1974 [63]

Suppose that there were a voting procedure that offered a straightforward strategy to every voter, whatever his preference scale .... A straightforward procedure would have immense advantages. No voter would ever need to hesitate how to cast his vote: the outcome of the voting would never depend upon the voters' erratic predictions how others are going to vote. We might well be willing to tolerate considerable deviation from the fairest outcome for the sake of such advantages.

Michael Dummett, 1984 [40]

Situations often arise in which groups must make a decision between three or more alternatives. However, there is no uniquely optimal way to make such a decision. A wide variety of voting methods have been proposed: some take into account only each voter's first choice, some take into account complete preference orderings, and some take into account the intensity of preferences. There are many techniques for aggregating preference information; often the election outcome is highly dependent on the voting method used. Advances in computer and telecommunications technology make feasible new techniques for collecting and aggregating ballots. In this dissertation we explore a novel group decision-making procedure made practical through such advances, and examine its ability to improve the decision-making process.

In a traditional election with three or more alternatives, some voters develop personal strategies to determine which alternative to select [24]. These strategies may take into account the voter's preferences for each candidate and the voter's estimate of the likelihood that each candidate will win the election. For example, voters may develop a strategy in which they vote for their most preferred alternative only if they believe that candidate has a ``good chance'' of winning. As illustrated in Figure , these voters may consider the results of pre-election polls to determine which alternatives meet their good-chance criteria before mentally evaluating their strategies. They express the result of this personal decision-making process in the form of a vote. However, traditional election results cannot distinguish between voters who vote for their sincerely preferred alternative regardless of other factors and those who base their votes on a strategy such as the one described above; this dilemma frustrates attempts at analyzing election results. In addition, inequalities in voters' access to information about the preferences of other voters and in knowledge about how to formulate optimal strategies may result in some voters having more power to influence the outcome of the election than their less informed peers.

  
Figure: Voting strategies in traditional elections

We present declared-strategy voting (DSV), a novel group decision-making procedure in which preference is specified using voting strategies -- first-order mathematical functions that specify a choice in terms of zero or more parameters. In a DSV system, illustrated in Figure , each voter submits a strategy that a computer resolves into a simple choice by substituting actual values for parameters. Parameters may include the percentage of counted ballots that select a particular candidate and the percentage of ballots already counted (or other measures of the ``maturity of the election''). In Chapter 4, we present the design of an automated strategy formulator that will produce an optimal strategy for every voter from straightforward inputs.

  
Figure: Voting strategies in declared-strategy elections

When a decision must be made between three or more alternatives, the outcome can depend on the voting method used. For example, plurality voting selects the alternative most preferred by the most people, while Borda count voting tends to produce more of a compromise alternative (both of these procedures will be described in Chapter ). But every non-dictatorial and deterministic voting method is subject to manipulation by voters who develop mental voting strategies and cast votes that misrepresent their sincere preferences. Declared-strategy voting dramatically reduces the opportunities for voters to benefit by misrepresenting their preferences, thus providing analysts with more accurate information about the true preferences of the electorate than can be obtained with traditional voting systems. This, in turn, may provide policy-makers with more accurate information on which to base their decisions. In addition, by minimizing the advantage gained by voters with access to the information needed to manipulate, declared-strategy voting provides voters with more equal opportunities to influence the election outcome.

Declared-strategy voting may be used in situations in which a single policy-maker bases a decision on the results of a non-binding survey, as well as in situations where a group makes a decision through a binding vote. Thus, the use of DSV may affect the ability of policy-makers to make the best decision, the ability of voters and survey respondents to express their preferences effectively, and the ability of analysts to interpret election results. DSV also impacts the result of the decision-making process itself, and thus affects all those for whom the decision is relevant.

The goal of this research is to determine whether declared-strategy voting can be an effective tool for group decision-making. This research focuses on exploring and refining the declared-strategy voting concept, assessing the potential impacts of declared strategy voting, and evaluating the effectiveness of declared strategy voting for group decision-making. This research makes several contributions:

• Throughout this dissertation we describe a new voting paradigm, declared-strategy voting. This paradigm enables voters to cast votes that are simultaneously effective and expressive. It also allows preference intensities to be considered in the vote aggregation process without relying on interpersonal comparisons of cardinal utilities.
• In Chapter 4, we introduce a new method for calculating pivot probabilities, the 2-D Gaussian method. This method easily scales for use in elections with a large number of alternatives. It has applications not only for DSV, but also for other social science work involving pivot probability calculations.
• In Chapter 4, we also present an automated strategy formulator. This formulator is important for making DSV accessible to the general public. It may also be useful for voters who wish to vote strategically in traditional elections.

This dissertation is organized as follows. Chapter  provides background information about many types of vote aggregation and ballot collection systems and introduces terminology that will be used throughout this text. Chapter  explains the motivations for declared-strategy voting and the overall design of a DSV system. Chapter  presents the details of rational-strategy formulation. Chapter  evaluates DSV and presents some examples of its use. Chapter  presents our conclusions and proposes areas for future work.