The goal of maximizing voting power while minimizing manipulability seems to be an elusive will 'O wisp.
However, in committees and other small groups one option is repeated balloting. For example, approval ballots can be repeated N times or until the ballots stabilize, whichever comes first. One problem with this method is that when there is no Condorcet Winner, the ballots may cycle radically, and the N_th time cutoff more or less randomly chooses a member of the cycle. When approaching the N_th balloting, various factions may try to trick others with feigned mutual support right up to but not including the last ballot. Or on the other hand, they may stubbornly bullet up through the penultimate balloting hoping that they will be used as a lesser evil compromise on the last vote by other factions. In other words, repeated approval balloting can be a game of chicken or prisoners dilemma or high stakes poker. Repeated plurality balloting is worse, yet that is what Lorrie Cranor used as her main example of Declared Strategy Voting (DSV). It seems to me that it would add stability and remove some of the high stakes poker feeling if the approval totals were accumulated for each candidate, and that the win would go to the first candidate to reach total approval of, say, K*M, where K is the number of candidates and M is the number of voters. After each balloting the cumulative approval totals of the candidates would be shown in a bar graph, with previous levels marked by color changes, and the K*M goal clearly marked as well. The voters would have a good enough idea of the progression to make a reasonable decision of how far down to approve in the next balloting. Drastic last minute changes in strategy would not be enough to make up for the cumulative trend, so approval increments would not gyrate wildly. How does DSV relate to this? The proposed version of DSV (Cumulative Repeated Approval Balloting Declared Strategy Voting or CRAB_DSV) would take as input each voter's relative utilities for the various candidates in the form of some kind of CR ballot, say the Five Slot Grade Ballot (possibly with plus and minus options for more resolution). The first balloting would be on the basis of each voter approving each of his/her above mean utility (i.e. above average grade) candidates. The subsequent approvals would be made with decision theoretic methods applied to the grade ballots in conjunction with the candidates' approval statistics, i.e. the statistics described by the bar graphs mentioned above. I believe that CRAB_DSV would overcome most if not all of the disadvantages of the version of DSV that Ms. Cranor devoted most of her attention to in her dissertation. In particular, it has the stability of her stochastic ballot by ballot version and the repeatability of her non-random repeated balloting version. Since Cranor's DSV was based on plurality, it bore a certain similarity to IRV, though less manipulable. Imagine doing repeated plurality balloting. Compare that with repeated approval balloting, and finally compare that with cumulative repeated approval balloting, and I think you can see a definite progression towards stability. Cumulative repeated plurality balloting would add some stability to Cranor's version, but it seems to me it would be the stability of getting into a rut, and being unable to move to a better rut, whereas approval doesn't penalize tentative testing of the waters in various directions in search for a better equilibrium. CRAB_DSV would allow voters to submit sincere grade ballots without fear of regret. The decision theoretic calculations automatically optimize the approval votes according to the information that becomes available at the end of each round of repeated balloting. Sophisticated voters have no advantage over the naive. If they think they do, they can limit their grades to A's and F's, for example, and the DSV calculations will automatically cast each of their ballots with all A's translated as approvals and all F's translated as non-approvals. The method is not summable in polynomial size data structures, but an approximation can be done in O(K^3) where K is the number of candidates. That's enough for now. Forest