[EM] Arrow's theorem and cardinal voting systems

Kristofer Munsterhjelm km_elmet at t-online.de
Sat Jan 11 03:48:32 PST 2020

On 10/01/2020 12.41, Steve Eppley wrote:

> For the criterion that matters most to me, I don't have a rigorous definition.  Here's a non-rigorous definition:  The voting method should give candidates who want to win a strong incentive to take positions that the voters themselves would collectively choose given a well-functioning direct democracy... even on issues that most voters don't care strongly about.  Here's how I relate that to voting methods like Maximize Affirmed Majorities (MAM), which facilitate competition, count all pairwise majorities, and pay attention to the sizes of the majorities:  Suppose candidate Alice wants to win, and is considering taking position p on some issue.  Although she knows a majority of the voters prefer alternative q over p, her wealthy campaign donors favor p and most voters care more about other issues.  Given a voting method like MAM, the risk to Alice is that by advocating p, she would create an opportunity for another candidate Bob to enter the race, take position q and copy
> Alice's positions on all other issues.  The larger the majority who prefer q over p, the larger the majority who would tend to rank Bob over Alice.  Defeating Alice.  A deterrent against taking unpopular positions to benefit donors.

How about this? If you clone A into A1 (Bob) and A2 (Alice), and A1 is
ranked above A2 on more ballots than A2 is ranked above A1, then if the
original winner was A, the new winner should be A1.

That most voters care about other issues than p vs q means that Alice
and Bob should be near-clones, since "Alice but with q" is a slight
improvement to "Alice with p", but not enough of an improvement that
some other candidate is ranked between A1 and A2.

If voters care more about q vs p, then A1 and A2 will no longer be
near-clones, but hopefully the method should generalize robustly from
the clone case so that it follows the spirit of the criterion.

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