thematics, we write down axioms and rigorously derive theorems from them. In science, on the other hand, we basically guess - or "hypothesize" [Sean Carrol, p. 222 of Space, Time and Motion]
Carrol's point is that in science, just as in mathematics, you begin with assumptions. But in science but in science, the assumptions eventually must be tested and re-examined. Regardless of how careful the reasoning is, there is always a possibility that some underlying assumption is simply wrong.
In this respect, voting should be thought of as a science. We can hypothesize and reason elections, but we must make assumptions about how voters will behave and those assumptions about voters must always be considered tentative.
In this light, I should apologize for occasionally overstating the merits of BAV (Balanced Approval Voting). I have suggested that adopting BAV will bring about the end of the duopoly. I still believe that, but I should point out an underlying assumption that may be wrong.
One might imagine, for example, that most voters fervently want the duopoly to continue as it is. So, faced with a BAV election the voters might vote in opposition to all candidates other than those nominated by the two dominant parties. If such would happen, the duopoly would surely survive. But if that is what the voters want, BAV would be doing what a good voting system should do in a democracy.
A good voting system gives voters what, on balance, they want, and BAV seems more than adequate in that regard. Enforcing an end to duopoly is key to a better democracy; I believe that and I think BAV will put an end to duopoly. But that judgement rests on an assumption that voters generally would prefer to have more candidates on their ballots; I do not know that for certain, so however remotely, it seems possible that this assumption is mistaken.
My attention to this issue stems from an article by Clay Shentrup, an enthusiastic supporter of (unbalanced) Approval Voting (UAV). The crux of his argument seems to be in one of his bullet items regarding BAV:
- [Knowledgeable] voters, faced with candidates they've never heard of, have a choice: leave them blank (giving them a free point) or mark "oppose" (giving them zero). A voter who understands the system will oppose unknowns rather than gift them points.
In accordance with what Shentrup suggests, some voters may choose to actively oppose any candidate they don't know or are ambivalent about. But others might vote for a candidate they don't know out of the feeling that even a candidate they don't know would be better than one they know to be a terrible choice. And others may disapprove of both duopoly candidates or perhaps greatly favor the idea of more competition; such a voter might choose to vote in opposition to both sides of the duopoly while supporting all the less-familiar candidates.
And it is certainly possible that voters may even do as they are advised and simply skip over candidates when in doubt. Neither Shentrup nor I can know how voters will behave BAV. Such insight would only be possible through studying elections conducted with BAV.
But as for the mistaken notion of a "gift", a knowledgeable voter will surely recognize that this notion of a "gift" is mere illusion. The so-called "gifted" points have no effect on the election outcome. This is because that very same gift is given uniformly to all the candidates, no matter how the ballots are marked. This results merely in each candidate's vote tally increasing by the same amount. That change can have no bearing on the election outcome.
So, I must object to Shenstrup's suggestion that not marking support or oppose on a BAV ballot amounts to "gifting a point" to that candidate. It quite decidedly does not; in a BAV election (as described), that ballot entry is simply skipped over when tallying the ballots so there is no way possibly for it to affect a tally.
Shenstrup's mistake comes from ignoring BAV as it is defined, but instead addressing an alternate representation; in fact, he chooses a representation which distorts appearances and creates the illusion. Instead of addressing BAV as it is properly defined, he considers score voting using the three scores [0,1,2].
But clearly, the more natural score interpretation, one that more in concert with the definition of BAV, would use the scores [-1,0,1] and with that better choice, the illusion vanishes. Adding the middle score of zero leaves the tally unchanged.
These two different score representations are equivalent in the sense that they produce the same winners and losers, but it is the [0,1,2] presentation is what contributes the unnecessary confusion.
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