I think the cited writing errs by assuming that an election ballot is asking the voter for an opinion. An election for office is not an opinion poll. Rather, it is an exercise in political power. Its purpose is to settle a disagreement about who should fill the office in question. Cohen argues that the meaning of the ballot to the voters is determined by the labels placed by the places on the ballot where the voter is permitted to make a mark and have it count. But I argue that the meaning of an election, and therefore the meaning of the ballots (both before and after they are marked) is to be found in the electoral outcome. This outcome may include not only the crucial fingering of which candidate gets to take office this time, but also possibly some numbers showing the public something about how well or poorly the losing candidates did. Such numbers can influence how citizens think about the popularity of the ideas espoused by the losing candidates and that can influence the voters for future elections. A third party can, conceivably, with some voting systems, show a gradual increase in popularity until they could start to win offices, a phenomenon that is all but impossible with the current system (and arguably, won’t happen in IRV either).
I think there is reason to expect that within a few elections of any new voting system being put into practice, the voters will learn the connection between the ballots and the outcome well enough so that many of them will learn at least one of the strategies for voting that within that given system, is likely to help promote that voter’s values, even when the voter does not trust other voters to cooperate and thinks that the other voters don’t expect the said voter to cooperate with them, either. That is, the voters know that they have no way to have a coordinated strategy in voting, so their best bet is to use the best individual strategy permitted by the system. Voters learned long ago that when the system is choose-one plurality, a non-major-party candidate such as Ralph Nader must be discouraged from running, and anyone voting for him is effectively voting Republican. So I’m expecting that just as the voters learned the best strategy for that system, it will occur to them what is the best strategy with a new system. And that best strategy cares not one whit what the labels are on the choices, nor on what intermediate accounting system is used to calculate the outcome. All it cares about is what is the freedom of movement accorded the voter, and within that freedom, no matter how the options are labelled, how do they affect the outcome.
I don’t oppose three-valued Score, which is the essence of what Cohen calls “Balanced Approval Voting” (a name that suggests that plain Approval Voting isn’t “Balanced”, even though it clearly exhibits Frohnmayer Balance, which is the kind of balance that is determined by the political power of the voters). I think there’s almost never a good strategic reason to choose the middle value, but even so, there is nothing wrong with the system. It delivers to the voters, individually, voter by voter, the exact same political power that plain Approval Voting* delivers.
Cohen says that if I change the numbering used in the intermediate steps of the calculation, or even if I argue by asking him to even imagine for the sake of discussion that these are changed, that I am putting over a sleight of hand, even though the outcome would not be changed. But I see no sleight of hand here, on the grounds that the election is not an opinion poll, and on the grounds that the outcome is not changed, and that the outcome embodies all the meaning of the election, once the voters have caught on to the power relations created by the voting system in question.
*I caution that the abbreviation “AV” doesn’t unambiguously mean Approval Voting, because in the UK, they use “AV” to mean IRV (as “Alternative Vote”).