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

Jameson Quinn jameson.quinn at gmail.com
Fri Jun 7 08:51:21 PDT 2013

I'm sorry, I don't want to get into an interminable back and forth with
someone who misuses my name and doesn't apologize, and prefers "you didn't
prove it!" to working anything out for themselves or asking nicely for


2013/6/7 Abd ul-Rahman Lomax <abd at lomaxdesign.com>

> At 06:28 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>>
>>  Subject was: Re: [EM] Someone thinks that Approval should meet the
>> Mutual Majority Criterion
>> James does not help us out with a description of why it fails.
>> Should I start calling you Joe now? :)
> You may join any club that will admit you. Ask Michael.
>  Others have said how it fails: through a turkey-raising strategy.
>> Implausible, unlikely, as you may have it; but still clearly possible.
> Actually, that was not said recently. It's not only implausible, it does
> not appear to violate FBC. That is why I have asked for specifics.
> Favorite Betrayal Criterion:
> Wikipedia:
>  A <http://en.wikipedia.org/wiki/**Voting_system<http://en.wikipedia.org/wiki/Voting_system>>voting
>> system satisfies the Favorite Betrayal Criterion (FBC) if there do not
>> exist situations where a voter is only able to obtain a more preferred
>> outcome (i.e. the election of a candidate that he or she prefers to the
>> current winner) by insincerely listing another candidate ahead of his or
>> her sincere favorite.<http://en.wikipedia.**org/wiki/Favorite_betrayal_**
>> criterion#cite_note-1<http://en.wikipedia.org/wiki/Favorite_betrayal_criterion#cite_note-1>>[1]
> Scorevoting.net (article by Ossipoff and Smith):
>  Voters should have no incentive to vote someone else over their favorite.
> After my usual carping about absolute standards like "no incentive" --
> Space Aliens can provide strong incentives -- I don't see how a
> turkey-raising strategy with an Approval primary involves betrayal of the
> Favorite. It does involve "betrayal" of a lower preference.
> I.e., primary unconditionally feeds top two to runoff, which is
> vote-for-one. I.e., this is the Arizona system, without the Approval
> feature.
> Voter prefers A>B>C. Voter fears that if runoff is A vs. B, B could win,
> so votes for C. This voter is going to wet his or her pants if C leads,
> but, never mind, maybe in the runoff A will win, because these turkey
> farmers are not going to vote for C in the runff.
> But, now suppose this is an Approval primary, i.e, this is in Arizona and
> it's a municipality that's implemented the system.
> Never mind that turkey raising is something that turkey farmers in Arizona
> would never admit to. Out in the Arizona desert, folks get along, and are
> straightforward and honest with each other. But, just suppose they try this.
> Okay, how does it show up? They could vote for C, hoping to push B out of
> the runoff. They actually can't do that, because of write-ins, which are
> allowed, but, hey, they can dream, they could even dream of Space Aliens
> telling them to vote this way. In fact, given that this is Arizona, that's
> fairly plausible. Something about the cloud formations. No, wait, that's
> New Mexico.
> But a little detail about FBC. Sure, they could vote for C, but if what
> they want is for A to win, which is the whole motivation for running this
> devious plan, why don't they also vote for A? They are pushing for B to be
> excluded, and, this way, they push with two candidates (or more).
> from the Smith-Ossipoff page:
>  one can prove FBC-compliance by the following strategy: If betraying
>> favorite F in order to make X win is the plan, and if that plan actually
>> works, then the alternate non-betrayal plan of simply raising X to be
>> co-equal top with F (carried out by the same set of voters who planned to
>> betray F, using the same set of votes they planned on) also works to make X
>> win. Q.E.D.
> There is no incentive to vote C above A, the favorite. Want to raise the
> turkey, C, to exclude B? Fine. Also vote for A. No Betrayal.
> Indeed, this is part of a more sophisticated system of utilities. A voter
> who votes A,C is *actually preferring to see a runoff between A and C* over
> B winning. They may *say* that they prefer B>C, we might speculate this
> about them, but the Space Alien in their head has convinced them to vote
> otherwise, and we don't know that there is anything in there except Space
> Aliens.
> If they think they need to bullet vote for C, they are not merely raising
> turkeys, they *are* turkeys. That should be part of FBC: the voters must
> not be turkeys. (Actually, it is, just not stated that way. There is some
> debate about complex strategies, blah, blah. It's moot here, unless someone
> wants to assert such a strategy.)
> Turkey raising strategy is FBC violating in non-approval top two runoff,
> but is risky there. Essentially, the faction that decides to do it must not
> be large enough to whack A by voting for C. It would, therefore, take
> collusion to be reasonably safe, and it would, therefore, risk losing A
> supporters. (Does A tolerate this? B just might start getting a lot more
> votes, and A might have trouble remaining in the top two. And if we really
> want to study this, we'd need to start looking at underlying utilities. And
> here we can start to recognize how blanket judgement of voting systems by
> simplified criteria can be a hazardous business, which was my original
> point on the CES list.)
>  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
>> difference.
> Of course we should be clear. If a system *technically* violates a
> criterion, but does not substantially do so, we should say exactly that. We
> would never say that it does not violate the criterion. However, here, an
> approval primary does not appear to violate the criterion. The "betrayal"
> is of a lower preference, not the Favorite.
>  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.
> Once again, it appears to me that Jameson is asserting this because he has
> not looked at an actual example, but is running off steam from *other
> situations.* There was no "explanation above." There is now. If it's not
> what Jameson had in mind, he's completely welcome to supply the scenario
> and explanation. For reference, here is "system 1", as defined by me and
> quoted by Jameson:
>  1. Top two approval where two candidates advance to the general election.
>> This fails FBC.
> QNED, quod non erat demonstrandum, this is not demonstrated.
>  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.
> "Election process" reasonably includes any process prior to a
> deterministic poll. The primary is, then, "part of the election process,"
> but is not the deterministic poll. We do not state that a voting system
> fails a criterion merely because of voting system details that still allow
> the test of the criterion. As an example, I have often claimed that
> repeated ballot, no eliminations, majority required to complete, satisfies
> the Condorcet criterion. This obviously must apply to the final poll, not
> to prior ones, because voters can and will shift their preferences, new
> candidates may be nominated, etc. It would apply to any *persistent*
> preferences, if expressed consistently. The definitive test is in the final
> poll.
>   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.
> Well, ontologically, "right" and "wrong" are only words, meaningless
> outside of definitions, not absolutes, but rather stands, judgements,
> opinions, models, etc., that are either useful or not. And this, too, is a
> stand.
> "Authoritarian" might be thought of as "bad." Not if one is an authority
> and is careful! Helpful authorities will explain the foundations of their
> knowledge.... and if they overlook this, they will surely provide it, when
> asked, if practical.
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