[EM] Does Top Two Approval fail the Favorite Betrayal Criterion

Abd ul-Rahman Lomax abd at lomaxdesign.com
Thu Jun 6 16:35:33 PDT 2013

Subject was: Re: [EM] Someone thinks that Approval should meet the 
Mutual Majority Criterion

At 01:56 PM 6/6/2013, Jameson Quinn wrote:

>2013/6/6 Abd ul-Rahman Lomax <<mailto:abd at lomaxdesign.com>abd at lomaxdesign.com>
>Another issue that was left a bit hanging in discussions on the CES list:
>Does top-two Approval fail the Favorite Betrayal Criterion? There 
>are really two forms of top-two Approval to be considered, plus a third detail.
>1. Top two approval where two candidates advance to the general election.
>This fails FBC. I am sympathetic to Abd's arguments about how the 
>electorate will change based on preference strength, and how 
>well-informed voters will tend to find a way to avoid FBC failure, 
>but that doesn't mean that it passes the criterion, merely that the 
>failure is minor.

James does not help us out with a description of why it fails. 
Further, "failure is minor" is an issue when using voting systems 
criteria to study voting systems. That's the problem with using the 
criteria as absolutes.

I did not give examples because I'm not asserting failure. Someone 
who is asserting it, I'd prefer that they at least show an example. 
It would be generous to cover the underlying utilities motivating the 
behavior, but I'll do that if the writer doesn't. (Or will infer them 
and might show that they do not significantly motivate the behavior, 
as a rough and nonspecific analysis is telling me.)

>2. Top two approval where a candidate with a majority can win, 
>otherwise two candidates advance.
>Still fails, although it's slightly better.

 From what point of view? *How* is it better? *How much* better?

>3. If write-in votes are allowed in the runoff, the primary is 
>actually a nomination device, not the actual election. The actual 
>election being Approval, the combination must satisfy FBC if 
>Approval does, and it does.
>This is true... but only if there's a hard threshold for making it 
>to the second round. That is, "all candidates with over 1/3 approval 
>advance", or some such; and if there are fewer than 2 such 
>candidates, the highest approval wins in the first round.

No. Threshold has nothing to do with it. If the primary is only a 
nomination device, it is like petition requirements or partisan 
primaries. Understand that this is like the Arizona proposal, but 
with Approval in the final election. If the final election is 
Approval, Approval satisfies FBC, because the voters may still vote 
for their Favorite in the general election. There is no cost to that, 
and by the rule that a method satisfies FBC if there is a simple way 
for the voter to actually vote for their Favorite and not betray the 
Favorite by voting for someone else *over* the Favorite, and gain as 
good an expected result, then FBC is satisfied.

>(If write-in votes are allowed, in this concept, the runoff must 
>also be Approval.)
>Arizona had a method up for legislative passage that would have 
>allowed municipalities to use a two-stage voting system with an 
>Approval primary, top-two advancing to the general election with 
>ballot placement, and, apparently, write-ins allowed in the general 
>election (as well as in the primary). The primary has no majority 
>test, it is top-two plurality, but voters may vote for as many 
>candidates as they choose. The runoff is standard vote-for-one.
>So, first of all, does this method fail FBC? If so, is the scenario 
>plausible for real voters? These are nonpartisan elections.

I'm not seeing any actual analysis here, just authoritarian statements. 

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