If there were a way to elicit sincere preference information from all voters prior to an election, this information could be made public and all voters would have the opportunity to use it in formulating their strategies. In the absence of sincere preference information, information about the strategies the other voters plan to use (sincere or otherwise) is still useful. However once the information is published, voters will adjust their strategies to take into account the preferences of others. Myerson and Weber [18] describe a series of polls in which voters are given the results after each poll. Eventually, they predict, a voting equilibrium may arise in which ``the perceptions arising from the publication of the poll lead the voters to behave in a manner that in turn justifies the predictions of the poll.'' They then go on to prove that at least one voting equilibrium must exist in all elections. In this scenario, all voters have equal access to the information that they need to vote strategically. However, conducting an election in this manner is unattractive because it would require voters to go repeatedly to the polls. This sort of election is likely to take a long time and have low voter turnout.
One way to side-step the problem of supplying voters with equal access to information is to allow them to cast votes that are contingent on the votes of others. While some parliamentary voting rules allow absent voters to cast proxies that are contingent on the votes of others (for example, the system used by the French National Assembly [9]), contingency voting is not a feature of most voting schemes. Contingency voting has a fundamental problem in that non-contingent votes must be counted before contingent votes; if all voters wish to cast contingent votes there is no way to count any votes without introducing an element of chance to decide which votes to count first. Another problem with contingency voting is the difficulty in evaluating complex contingency rules, especially when the number of voters is large or when votes are tallied at many geographically distributed precincts. But contingency voting is nonetheless appealing because it allows voters without voter preference information to vote strategically. In addition, examination of contingency votes may provide insight into the true preferences of the electorate that is not otherwise available when voters vote insincerely.
The advent of high speed computers and computer networks makes it feasible to tally contingency ballots in a reasonable amount of time. In addition, computers can handle complicated vote aggregation methods, making possible voting procedures not previously considered. With that in mind, we now sketch the design of an information-neutral voting system that employs contingency voting. We shall call this system a declared-strategy system because voters declare the computations used to determine their vote. The computation represents the voter's strategy in formulating a vote, rather than simply the outcome of that decision process. Following game-theoretic practice, we assume that each voter decides on a strategy prior to the election that includes a specification of how the vote will be cast given any contingency. A declared strategy is a first-order function of the ``state'' of the election. In our system, voters will vote by submitting their strategies to the election computer. The computer will evaluate the voters' strategies using the current election tally and other state information. The strategies will then be aggregated to determine the election outcome.
In analyzing the declared-strategy voting system for rational votes, the following components must be defined: