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:

- the set of permissible strategies that voters may submit,
- the method for calculating the probabilities of the various contingencies, and
- the method for aggregating the strategies of the entire electorate.

Thu Apr 25 14:31:14 CDT 1996