[EM] Does Top Two Approval fail the Favorite Betrayal Criterion
Abd ul-Rahman Lomax
abd at lomaxdesign.com
Fri Jun 7 09:25:18 PDT 2013
At 06:28 PM 6/6/2013, Jameson Quinn wrote:
>2013/6/6 Abd ul-Rahman Lomax <<mailto:abd 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:
>A <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
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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