The last part of our declared-strategy voting system that must be considered is a method for aggregating the strategies of all voters. We have considered two types of aggregation techniques: ballot-by-ballot and batch. Both of these techniques may be combined with any traditional aggregation technique (plurality, approval, Borda, etc.).
The ballot-by-ballot technique involves making an outcome prediction,
evaluating one randomly selected ballot based on that prediction,
updating the prediction, and repeating until all ballots have been
evaluated. The initial prediction may be based on the sincere outcome
point. (Alternately, the initial prediction may be set to 0, however,
this seems to result in outcomes which are quite dependent on the
first few ballots selected for evaluation.) As the ballots are
evaluated, they should be added to a running tally. This technique
results in outcomes which are somewhat dependent on the random
evaluation order. Thus the election results may not be stable, a
problem which render this solution unacceptable for many elections
situations.
The batch technique involves making an outcome prediction based on the sincere outcome point, evaluating all ballots based on this prediction, updating the prediction based on the previous evaluations, and repeating until an equilibrium is reached. This technique simulates the situation described by Myerson and Weber [18] in which voters are repeatedly polled until the results of a poll justify the predictions of the previous poll. The batch technique is preferable to the ballot-by-ballot technique because it does not introduce chance into the declared-strategy system.