[EM] An incentive to take positions a direct democracy would choose (was Re: Arrow's theorem and cardinal voting systems)

[Steve Eppley]

On 1/11/2020 6:48 AM, Kristofer Munsterhjelm wrote:
> 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.

If by "How about this?" you're suggesting satisfaction of that clone criterion ("... the new winner should be A1") implies satisfaction of my non-rigorous criterion ("create a strong incentive to take positions the voters would choose"), I don't see why that would be so. 

Instant Runoff would elect A1 in that clone criterion's scenario, yes?  But Instant Runoff doesn't create the incentive.  To the contrary, Instant Runoff defeats candidates who advocate compromises that voters would collectively choose, and makes those candidates & positions appear unpopular.  Instant Runoff rewards extremists the same way Plurality Rule does, because it counts at most one of the majorities, which can be a coalition of minorities.  For example, a minority who want abortion banned, plus a minority who want immigrants deported, plus a minority who want guns unregulated, plus a minority who want capital gains taxes slashed, etc, can together add up to a majority.

--Steve