[EM] RE: simplifying ballots

[Simmons, Forest]

Abd ulRahman Lomax proposed:

The proposal is that the ballots might be counted first as ordinary
approval. If a majority appears from this process for a given candidate in
a single-winner election, the candidate would be elected. If not, then the
ballots would be retabulated as fractional approval, i.e., if you voted for
N candidates, your vote would be assigned as 1/N for each of them, and then
it is ordinary Asset voting from that point.

Forest replies:

This seems like another good possible use of simple ballots.

I would like to point out that on this EM list, customary usage would substitute "counted cumulatively" for your phrase "retabulated as fractional approval."

Also on this list is has been pointed out from time to time that just as Approval is strategically equivalent to Range Voting, so Plurality is strategically equivalent to Cumulative Voting, now also called Fractional Approval.

But more recently I have noticed something very interesting along these lines.   If we interpret the cumulative vote as a mere restriction on the sum of absolute values, allowing both positive and negative values, then this version of cumulative voting becomes equivalent to "one vote for xor against" in which the voter can either cast a supporting or a detracting vote, but not both (hence the exclusive or). 

Note that in the three candidate case, this *xor* method is equivalent to ordinary approval.

So the "xor" method is strategically equivalent to range voting in the case of two or three candidates (but not in the case of more than three candidates).

One of the beauties of the "xor" method is the symmetry that allows husbands and wives to cancel each others' votes, no matter the number of candidates.

Plurality doesn't allow that except in a two way race.

Suppose that there is a close three way race among candidates A, B, and C, and the wife knows that her husband is going to vote for candidate A.  She doesn't know whether B or C is better, but she knows that if her husband is advocating A, then A is the worst candidate.

Under Approval or Range Voting she can cancel her husband's vote by awarding maximal values to all candidates except A (who gets the minimum possible value, usually zero).  Under "xor" she can vote directly against A.  But under plurality, ordinary cumulative voting (a.k.a. fractional approval), or even IRV she would have no way of cancelling her husband's vote.

Who will alert the League of Women Voters?

Now, what would happen if we used this "xor" method for asset voting?  How would we handle negative assets.  It seems like they should subtract from a candidate's positive assets, but what if a candidate has all negative assets?  Who decides how to spread these around?  (certainly not the despised candidate himself)  Is there any useful way to define negative representation?  How about imaginary representation? [Whatever it is, it seems like we have a lot of it these days.]

Forest

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