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Mousetraps

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Paul Cohen
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"Build a better mousetrap, and the world will beat a path to your door"

That appealing notion might have been justified when Ralph Waldo Emerson wrote the words in 1855, shortly before the civil war began.

But most commerce was local then. The internet did not exist and there were no televisions or radios. And what little advertising there was, lacked the psychological sophistication behind it today.

As a practical matter, during the early 19th century, a typical person's world rarely extended beyond the nearest community. News and opinions spread across that much smaller world mostly by word of mouth; there was no need to hire an advertising firm.

But in this larger, now global world, a new and better mousetrap could very easily go unnoticed. At the same time, the world could be beating a path to purchase a much inferior mousetrap due to its well-funded professional promotion.

If you have followed this series of articles, you might have guessed that "a better mousetrap" serves here as metaphor for BAV, the Balanced Approval Voting system.

BAV first occurred to me in 2014 and soon afterwards, I had a EUREKA! moment as I perceived the potential BAV has for undermining a two-party duopoly. That would at least dull the sharp edge of the toxic polarization that our society now suffers.

Subsequently, I did learn that others had mentioned this voting system and given it other names. That did not seem particularly surprising or important; it still seemed clear that too few people had ever given this voting system more than a passing glance. It was all too easy (though inaccurate) to simply dismiss BAV as merely one of the many score voting systems.

BAV clearly deserved much more attention than it had received. There seemed no alternative to accepting that as my personal challenge since it seemed hard to imagine that anyone else would.

That is the back-story of why I have written this series of articles. In writing them, I have come to more fully appreciate how BAV is such a superior voting system, and I have done my best to communicate that understanding to others.

I want to express my gratitude to Rob Kall and to OpEdNews for publishing these articles.

These efforts have had some success. At a minimum, four thousand people are now aware of BAV and judging from the number of downloads of these articles (Nearly 180,000) BAV must hold more than a passing interest from many people who know of it.

But clearly it is wrong to claim that the would is beating a path to BAV's door. And additional articles are not likely to change that. That will not happen without an aggressive advertising campaign.

An all-too-common belief is that ranked-choice voting is the best alternative, probably the only alternative to plurality voting.

But there are many other voting systems to choose from. Even for just range voting (also called score voting), there are infinitely many variations. But few people have even heard of these other voting systems. BAV, for example, has had no serious promotion aside from these articles.

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Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. (more...)
 

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2 people are discussing this page, with 4 comments  Post Comment


William WAUGH

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The mock election, the nationwide primary, these are good ideas, and any voting system that provides equality could be used. These measures could defeat the two-party system and defeat oligarchy. They could convert a mere republic into a democratic republic. Of course, we have to get our republic back from the Heritage Foundation and Donald Trump and their followers, who stole it.

I would like to return to your and my discussion about whether "indifference toward a candidate" is meaningful without indifference toward the election as a whole. You say that it is, and I say that it is not.

Suppose we:
  • collect BAV ballots;
  • see each ballot as scoring each candidate -1, 0, or 1, and rewrite the ballots (first transform) in that form, taking care to include with scores of zero, the candidates the voter did not mark;
  • take the arithmetic mean of the scores on each of the ballots resulting from the first transform, call that _a_[_v_], where _v_ identifies the voter.
  • transform the scores (second transform) by subtracting _a_[_v_] from each score on the ballot of voter _v_, across all ballots.
The tally is done in the usual way as any Range Voting system, but with the (second) transformed scores. Do you admit that for any set of ballots, the winner from this procedure will be the same as the winner would be from applying the BAV tallying procedure to the original ballots? And in fact, that the entire final ranking of candidates for purposes of understanding how well they did against each other will be the same for this procedure as for BAV?

Submitted on Sunday, Feb 1, 2026 at 9:07:44 AM

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Paul Cohen

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Of course. Mathematically, BAV as I have defined it is isomorphic with ranked voting with three equally spaced scores, provided that the middle score is the default assigned when the voter fails to assign one. But as I recall, my point in the earlier discussion was that from a typical voter's perspective, those two (mathematically equivalent) voting systems will often seem quite different.

Submitted on Sunday, Feb 1, 2026 at 3:02:28 PM

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William WAUGH

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Then do you see that if a voter's transformed ballot adds a positive number to a candidate's score, that candidate is advanced against the other candidates, toward the winning position?

Submitted on Tuesday, Feb 3, 2026 at 5:01:40 AM

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Paul Cohen

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I might add that with BAV, what you indicate, for each candidate, either support, opposition or neither. Whether you take "neither" to mean you are indifferent, or perhaps ambivalent, is just a word-choice; probably "neither" is more accurate.

But it is quite possible that there is one (or more) candidates that you put in that middle, "neither", category that you approve of the least and perhaps you had a mental debate whether to vote "oppose" for that candidate rather than neither. There are similar issues for each of the three positions, though "neither" experiences that with both of its neighbors.

Different voters will draw these lines differently between adjacent ratings, effectively giving the tally a way to take account of such shadings of each of the three possible assignments.

Submitted on Monday, Feb 2, 2026 at 4:50:40 PM

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