If DV is not chaotic I can definitely get behind it! Also, I guess there is a “limiting case” argument for proportional redistribution. For example, using the string voting as a crude model (supposing it is a reasonable representation of interests) you could assume that as the allowed number of characters gets arbitrarily large, voters will tend to approach a stable distribution among the candidates, i.e. far out in the string, the probability that a random character represents a particular candidate should depend only on the candidate. I think that’s a reasonable assumption, and in that case the long string method will, at first, conform to a discrete analogue of proportional redistribution in terms of costs to voters. And if the marginal costs are distributed more-or-less proportionally, then so should be any marginal gains.
I agree that the string method is more theoretical than practical. It allows voters to control their marginal utility functions for a small number of discrete votes, but for proper redistribution you would want to be able to analyze the marginal utility functions for an arbitrarily large number of discrete votes. Pushing the characters to the left achieves some level of redistribution, but the problem is illustrated in the example I gave, where Voter 1 at some point in the algorithm ends up with a string like AAAAAAAXXXX, and hence one of their available votes isn’t counted at all. If they had submitted a longer string, basically “loading up” the marginal utility function beyond the characters that are counted in the algorithm, they would have a better chance at having their votes fully redistributed according to their marginal utility.
So I was thinking, maybe the theoretical voters could submit significantly longer strings, and then have the algorithm only look at the beginning portions, and allow the characters beyond that to slide into place when candidates are eliminated. But I think that opens the floodgate to tactical voting of the kind you suggested. When the strings are totally truncated, I’m not sure that tactical voting in that sense would actually be a good idea, because the tactical voter runs the risk of their alternative choices being eliminated early, and then having no fall-back if their first choice gets eliminated. So it’s risky. Basically I think honest voters would have more consistent control over the entire election, while tactical voters would have disproportionate control over the beginning stages, but then their influence would die out quickly.
The other method similar to DV I was thinking of is analogous to the string method, where voters incur costs in voting capital proportional to their investments in protected candidates. So again, rather than eliminated the least-grossing candidate, candidates are protected in turn, costs are incurred for protection, and then the final remaining vulnerable candidate is eliminated and remaining capital is redistributed. I think that would tamp down on strategic voting, but again I am not sure how it fairs in practice, and I know that there are problems with it. For example, if you have two voters with distributions
Voter 1: [1,0,0,0,0]
Voter 2: [0,1/4,1/4,1/4,1/4]
I think we can agree that the most rational approach to deciding a victor is to uniform-randomly select one of the four candidates that Voter 2 supports, and then select uniform-randomly between that candidate and the candidate that Voter 1 supports. But with incurred costs and redistributions, I think Voter 1 comes out on top, basically because Voter 1 incurs costs to protect his candidate once at the beginning of the first round, but then Voter 2 incurs costs three times for the remainder of the round before one of their candidates is eliminated and the points are redistributed. So vote-splitting exists. I don’t know how it works with many voters though. Vote splitting is avoided in DV because there are no incurred costs, but then there is the (minor?) risk of tactical voting.
If tactical voting is a very minor problem in DV, I think it turns out to be superior to a protection-cost/redistribution system. But if there were a way to incur costs without vote splitting, I think that would be a great theoretical development. I was having costs incurred basically like an auction against the average of the remaining candidates, but there might be a better way. For example, maybe voters pay the cost of the difference between the highest-grossing candidate and the second-highest, so it’s kind of a grass-trimming situation. I don’t know, just spit-balling here.