[EM] Schwarzenegger was Condorcet winner; VPR and Candidate Withdrawal to simplify voter strategy (was Re: Arrow's theorem and cardinal voting systems)

[Steve Eppley]

On 1/13/2020 6:32 PM, Forest Simmons wrote:
-snip-
> It's not just Approval that requires some hard thinking in conjunction with filling out the ballots. Ranking many candidates (think about the number of candidates in the election that propelled Schwarznegger into office) may be just as burdensome as trying to decide exactly which candidates to mark as approved. In Australia you can get around this difficulty by copying "candidate cards" or by voting the party line.
-snip-

During the week or so before Schwarzenegger was elected Governor of California (ousting Governor Gray Davis in a recall election), likely voters were surveyed by a team of grad students led by economics & political science professor Rod Kiwiet of Caltech.  The voters were asked the 6 pairwise preference questions regarding the 4 candidates judged by Kiwiet to be the top 4 (including Davis).  The survey result was that Schwarzenegger defeated the other 3 candidates pairwise.  A Condorcet winner.  So I don't agree that Schwarzenegger was "propelled into office by the (large) number of candidates" but perhaps I'm unaware of better evidence.

Regarding Australia's solution for their tedious lengthy STV PR ballot, a similar way to make strategy simpler for voters is to use a voting method in the Vote for a Published Ranking (VPR) family of methods: 

     Before election day, each candidate publishes a ranking of
     all the candidates (presumably with him/herself on top). 
     Any candidate who doesn't publish is disqualified.
     (Alternatively, any candidate who doesn't publish is treated
     as if s/he'd published the ranking that has him/herself on top
     and all other candidates tied at the bottom.)

     On election day, each voter votes by selecting one candidate.

     Each vote is tallied as if it were the ranking published by the
     voter's selected candidate (using society's favorite algorithm
     for aggregating voters' rankings).

Some potential advantages of VPR:
(1) Good candidates wouldn't need as much money to win, since they can win by persuading some "popular" candidates to rank them over worse candidates.  It might require only a few phone calls. 
(2) After the candidates publish their rankings, journalists & pundits would presumably scrutinize the rankings looking for unusual preferences, a possible sign of corruption.  Presumably many voters would learn about those oddities before election day, and reconsider who to vote for.
(3) It's relatively simple for the voters.  My hunch is that strategically-optimal votes would typically be votes for one's favorite candidate, even when there are many candidates.
(4) It solves problems related to "too many candidates" and "low information voters" -- in particular that the best candidates might be left unranked by a lot of voters.  It was this concern, expressed by Mike Alvarez of Caltech many years ago, which led me to propose VPR in an article published in 2007 in the Pasadena Weekly:  https://pasadenaweekly.com/roberts-rules-for-voting/  (In 2007, Rudy Giuliani was considered a frontrunner for the 2008 Republican presidential nomination, so his name appears in an example in the article.)

Two variants of VPR:
1. NGOs could publish rankings too, and be eligible for selection by voters on election day.
2. Given adequate technology in the voting booth... The voter begins by selecting one candidate.  The voting machine then displays that candidate's published ranking, and the voter may rearrange it. (A big time saver, yet the voter has maximal control over his/her ranking.)

Another way to simplify voter strategy is to allow candidates to withdraw from contention after election day, after the votes are published (in a summary format adequate to be tallied using the voting method).  A spoiler could choose to withdraw to help a compromise defeat a "greater evil."  The Candidate Withdrawal option would also make voting methods more compatible with the U.S. Electoral College, because candidates could withdraw to help a compromise candidate obtain a majority in the Electoral College.  A variant of Candidate Withdrawal is to allow candidates to withdraw from particular pairings while remaining in the other pairings (assuming a pairwise voting method).

Subscribers to Election-Methods may already be familiar with VPR and Candidate Withdrawal since they were discussed here many years ago.  I've read few messages in the last 10-ish years, so I have no clue about what current subscribers are familiar with.

--Steve