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

Jameson Quinn jameson.quinn at gmail.com
Thu Jun 6 16:28:49 PDT 2013

2013/6/6 Abd ul-Rahman Lomax <abd at lomaxdesign.com>

> 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>a**
>> bd 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.

Should I start calling you Joe now? :)

Others have said how it fails: through a turkey-raising strategy.
Implausible, unlikely, as you may have it; but still clearly possible.

> 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.

Yes, it's an issue. Absolutely. The difference between failing badly and
barely failing, is often larger than the difference between barely failing
and passing. But that doesn't mean you shouldn't be clear about the

> 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?

If any candidate has a majority, there is no FBC failure. If not, you have
system 1, which can fail FBC as explained above. Since that is only part of
the time, it is only partly as bad.

>> 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 the primary is not considered as part of the election process, then
sure, it could consist of shooting any candidate with an even number of
votes, and it would not cause FBC failure. But if you are considering it as
part of the election, you can't just make it up as you go along. A hard
threshold, or a threshold based on a mathematical function of the top
candidate's votes alone, causes no FBC failure. A set number of candidates
advancing causes FBC failure, though not a particularly serious one.

>  (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.

So? Right and wrong are not decided by word counts or votes.

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