My guess is that this isn’t a new idea, but there is a voting system concept I’ve been considering that is at the very least interesting to me. The way it operates is that a real number B in the interval (0,1) is chosen, and then voters are allowed to score each candidate independently with any one of the discrete values B^k for integer k from 0 to N, where no score indicated is by default B^0=1. In its most simplistic form, each candidate has all of their scores summed, and the candidate with the smallest sum of scores is declared the winner. Basically it’s just like simple score, but the values of the scores are weighted exponentially, and rather than the highest sum winning, it is instead the lowest sum.
This structure of scores has some interesting properties, in my opinion. Often people will point to min-maxing as a manipulation strategy that reduces the quality of score voting. However, if exponential scoring rather than standard scoring is paired with something like a STAR runoff, I have the present belief that both min-maxing and majoritarianism should in principle be significantly diminished.
Consider the simplistic version without a runoff. As in the normal score system, voters will do best to score their honest favorite candidate most favorably—in this case, giving them a score of B^N. At the same time, they would do best to score their honest least favorite candidate most poorly—in this case, giving them a score of B^0=1.
At this point, the most favorable score acts as a “source,” and the least favorable score acts as a “sink.” There is a strategic incentive for the voter to score all of the rest of the candidates poorly, so as to boost their most favored candidate’s chances of winning the election, or at the very least, there is incentive to categorize the candidates into “winners” and “losers,” and then to score the winners very favorably and the losers very poorly, which unchecked will naturally result in an approval voting process.
However, consider a collection of winners who the voter plans initially to score most favorably. In reality, it is unlikely that the voter is totally indifferent to these candidates, and probably there is a single candidate they most prefer. Hence, since the difference between the most favorable score value and the second-most favorable score value is very small compared to the values of most other scores (since they are exponentially decayed), the voter is much more likely to indulge in expressing this preference, however slight. But again, even the difference between the second place and third place slots are slight in comparison to the lower scores, which are exponentially larger. So there is an extended incentive to spread out their first several top choices in an honest fashion!
On the other end, suppose the voter wants to score all of the “losers” as poorly as possible. Again, it is unlikely that they are totally indifferent between these loser candidates. Probably there is one candidate that they would be least happy with winning the election. Since there is such a large gap between the last place and the second-to-last place slots, and since both slots are still sufficiently large compared to the upper tier score values, the voter can feel secure in indicating this preference in an effort to prevent their least-favorite candidate from winning over any of the others, and they can do this without really compromising the status of their top choices. The same goes for any other sufficiently strong preferences over candidates at the bottom.
So in an exponential score system, I believe there is more strategic contention toward the middle range scores than at either end. But in the middle, there is also less wiggle room for manipulation. I think voters would generally compromise their preferences starting from the top and the bottom, and those should in principle meet somewhere naturally in the middle. Compound these natural incentives and constraints with a runoff that gives even stronger incentives for indicating preferences, and I think such a system could do very well against min-maxing strategies and majoritarianism in the long-run.
Any thoughts are welcome.