[Version 3]

This is a proposal for a method of election of a single winner.

Prescription

The Ballot

The top of the ballot will sport a checkbox labeled “Tally from the top down.” If the voter does not check this box, the interpretation shall be “Tally from the bottom up”. I will explain the significance of this distinction under the heading of the tally, below.

The voter can rank the candidates. Equal ranking is allowed. If the voter fails to mention any candidates, the tally shall interpret the ballot as though it had an additional rank at the bottom mentioning the unmentioned candidates.

This completes the prescription of the voter’s freedom of movement in filling out the ballot.

The Tally

[Oops, I made a serious error in writing this section. For the moment, please refer to the previous version, linked at the bottom]

Design Motiviation and Analysis

Meeting the Balance Constraint

A balanced election system is one in which for every possible vote, there is another vote that would cancel the effect of the first vote. I believe that balance is necessary to resist the effect of expensive advertising. I believe that IRV advocates cannot bring a proof to the effect that IRV is balanced.

The present proposal meets the balance constraint. The antivote of a given vote turns its ranks upside down and toggles the direction-of-search control. The antivotes thus address the same candidates on a given round, and have the opposite effect on the accumulators.

Bottom-up ballots are based on hatred. They give priority to eliminating the worst candidates.

Top-down ballots are based on love. They give priority to supporting the best candidates, similar to IRV.

Division of the Individual Voter’s Political Power

An advocate for IRV brought me the critique that in Score Voting, if a voter gives any support to a compromise candidate, that can dilute the effective support given to the favorite candidate, depending on the other votes. I designed the present proposal to address this critique. A bottom-up voter gives her full political weight to the elimination of the terrible candidates, so long as they have not been eliminated. If there is sufficient agreement from the other voters that the terrible candidates can be eliminated, then the system allows the bottom-up voter to support her favorite candidates fully. Therefore it seems that the present proposal escapes this critique of Score Voting.

Election Mechanics

The present system cannot be tallied by the precincts. This increases the cost of an election as compared to Score Voting. However, the cost of an election is trivial compared to the cost of bad government caused by electing a bad candidate. It would be possible to do a tally where the actual counting happens in the precincts, but there would have to be a dialog between the precincts and the center after each round, to settle on the set of candidates remaining standing for the subsequent round.

Question

I understand that there is a theorem in Game Theory that implies that there is no voting system for which the best strategy is honesty, and no voting system in which the best strategy does not depend on the voter’s estimate of the other voters’ values with regard to the relative merits of the candidacies.

However, if the best strategy in Balanced Elimination Voting isn’t to honestly rank the candidates (allowing equal-ranking if one feels the same degree of support toward two or more candidates) and choose the bottom-up search, I don’t know what it is. This can’t always be the best strategy if my understanding about the theorem is correct.

Who can resolve this paradox?

[I previously described this system differently and offered more flexibility to sophisticated voters.]

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