[EM] PAR is awesome part 1/2: FBC?

[Jameson Quinn]

2016-11-13 6:34 GMT-05:00 C.Benham <cbenham at adam.com.au>:

> On 11/13/2016 3:35 AM, Jameson Quinn wrote:
>
> What I mean is that if you take a non-election-theorist, present an
> election scenario to them, explain who won and why, and ask how they would
> strategize in the place of voter X, they are more likely to suggest
> counterproductive strategies, and less likely to see any strategies that
> actually might work, in Condorcet than in Bucklin-like systems.
>
>
> The strategy incentives for Condorcet voting methods vary widely.  Some
> have a random-fill incentive while others have a truncation incentive. Some
> have
> a stronger or weaker incentive to equal-top rank than others, and some are
> more vulnerable to Burial than others.
>
> Smith//Approval has a truncation incentive like Bucklin's, only less
> strong. In addition Bucklin has an equal-top rank/rate incentive.  I don't
> see the problem.
>
> BTW, why does it matter if "non-election-theorists" when asked suggest
> "counter-productive strategies"?  Shouldn't we be encouraging sincere
> voting?
> If they don't want to do that, why can't they just take the strategy
> advice of their favourites?
>

My concern here is that people will misuse strategy. I think that FBC and
IIA are good guarantees to be able to give, but also that these guarantees
are related to O(N) summability, which is basically saying "you can think
about what's going on in an election, it fits inside your head." PAR does
not have O(N) summability, but it can be done in 2 steps, each of them O(N)
summable, and each of them considered separately meeting FBC and IIA.


>
> 35: C >> A=B
> 33: A>B >> C
> 32: B>A >> C
>
> In Smith//approval, one vote alone would shift the above honest election;
> so the fact that it does not in PAR is indeed notable.
>
>
> I don't see why.  The example I gave just happened to have a close CW.
> PAR seems to give an A=B tie unless (as I assume) it breaks tied final
> scores in favour of the "leader" (A).
>
> In particular: in PAR, there is no way for the B voters to strategize such
> that they win the above election, while still ensuring that C does not win
> no matter what the A voters do.
>
>
> Of course, that is why it's called a "chicken dilemma".  In what method
> *can* "the B voters to strategize such that they win the above election,
> while still ensuring that C does not win no matter what the A voters do" ??
>

I think that you still don't understand what I mean by "slippery slope".
(Of course, once you do understand it, you're still free to disagree that
it's important.)

Suppose you have a scenario like the following:
19: A>B
11: ??? A or A>B ??? (more generally: either a bullet vote for A, or a vote
with A top, B second-to-bottom, and all else bottom. In approval, then,
this would be A or AB)
25: (ego faction; true preferences B>A)
45: C

You are in the ego faction, and deciding whether to vote B>A or just B (or
in approval, BA or B). If there is some combination of votes that the ego
faction can give such that B wins in the case where the 11 votes are B>A,
but A wins in the case where the 11 votes are A, then there is a slippery
slope; the ego faction can safely and profitably use a small amount of
offensive strategy, which means that A voters should use slightly more
defensive strategy, and then there's a cycle of escalation until both
factions fall off the cliff and end up electing C.

Is that clear now?


>
> MJ passes IIA. PAR fails it, as you say, but passes LIIA.
>
>
> As do some Condorcet methods. It isn't one of the criteria I care much
> about.
>
> As I understand it, IIA can only be met by methods that fail Majority
> (like positional methods that pretend that the voters' ratings are on some
> scale independent of the
> candidates).   MJ  is a variety of Median Ratings which is normally
> claimed to meet Majority.
>

IIA, when applied to a cardinal or categorical method, assumes that when
you remove a candidate, you simply delete that candidate from all ballots
and leave them otherwise unchanged.

The definition of majority used in the proof that IIA and Majority are
incompatible assumes otherwise. Thus, this proof does not apply to
non-ranked methods. Or perhaps one could say: it shows that a method cannot
pass IIA and ranked-majority. MJ does not pass ranked-majority, but it does
pass majority, so that's fine.

MJ does pass IIA.

>
> I would be a bit surprised if IIA can be met by a method (such as MJ and
> Bucklin) by a method that fails Irrelevant Ballots Independence.
>
> There is some rubbish about Independence of Irrelevant Alternatives (IIA)
> on Electowiki.  I'll address that in a later post.
>
> Chris Benham
>
>
>
> On 11/13/2016 3:35 AM, Jameson Quinn wrote:
>
>
>
> 2016-11-12 10:45 GMT-05:00 C.Benham <cbenham at adam.com.au>:
>
>> On 11/12/2016 7:53 AM, Jameson Quinn wrote:
>>
>>
>>
>> 2016-11-11 12:50 GMT-05:00 C.Benham <cbenham at adam.com.au>:
>>
>>> On 11/11/2016 10:14 PM, Jameson Quinn wrote:
>>>
>>> I think that simple PAR is close enough to FBC compliance to be an
>>> acceptable proposal.
>>>
>>>
>>> I'm afraid I can't see any value in "close enough" to FBC compliance.
>>> The point of FBC is to give an absolute guarantee to (possibly uninformed
>>> and not strategically savvy)  greater-evil fearing voters.
>>>
>>
>> Yes. The guarantee you can give is "as long as the world is somewhere in
>> this restricted domain — that is, essentially, as long as there are no
>> Condorcet cycles and each voter naturally rejects at least one of the 3
>> frontrunners — this method meets FBC". This is much broader than any
>> guarantee you could give for a typical non-FBC method. For instance, with
>> IRV, the best you could say would be "as long as your favorite is
>> eliminated early or wins overall, you don't have to betray them", which
>> unlike PAR's guarantee is not something which could ever be generally true
>> about all real elections for all factions.
>>
>> C: I have in mind voters who are inclined to Compromise, and so it's *
>> absolute guarantee* or it's nothing.   Smith//Approval also has a much
>> lower Compromise incentive
>> than does IRV  (which in turn has a much much lower Compromise incentive
>> then FPP).
>>
>>
>>
>>
>>>
>>> It elects the "correct" winner in a chicken dilemma scenario,
>>> naive/honest/strategyless ballots, without a "slippery slope" (though of
>>> course, this is no longer a strong Nash equilibrium).
>>>
>>>
>>> How do you have a "chicken dilemma scenario" with
>>> "naive/honest/strategyless ballots" ?
>>>
>>> 35: C >> A=B
>>> 33: A>B >> C
>>> 32: B >> A=C  (sincere is B>A >> C)
>>>
>>> In this CD scenario your method elects B  in violation of the CD
>>> criterion.
>>>
>>
>> You're suggesting that the sincere preferences are
>>
>> 35: C >> A=B
>> 33: A>B >> C
>> 32: B>A >> C
>>
>>
>> C:  I'm not "suggesting". I'm stating.
>>
>>
>> If you are 1 of the B>A>>C voters considering whether to strategically
>> vote B>>A=C, you have no strong motivation to do so, because your vote
>> alone is not enough to shift the winner to B. This is what I mean by "no
>> slippery slope".
>>
>>
>> C: One "vote alone" is very rarely enough to do anything, so I suppose
>> no-one has a "strong motivation" to vote.
>>
>
> In Smith//approval, one vote alone would shift the above honest election;
> so the fact that it does not in PAR is indeed notable.
>
> In particular: in PAR, there is no way for the B voters to strategize such
> that they win the above election, while still ensuring that C does not win
> no matter what the A voters do. This "safe" strategizing is grease on the
> slippery slope.
>
>
>>
>>
>> I believe that in the election you gave, there is no way to tell what the
>> sincere preferences are.
>>
>>
>>
>> C: From just the information on the ballots, of course not (like any
>> election).
>>
>>
>> Perhaps the B voters are strategically truncating A; perhaps the C voters
>> are strategically truncating B. So the "correct winner" could be either A
>> or B, but is almost certainly not C.
>>
>>
>> C: By "correct winner" I assume you mean the sincere CW. But there is
>> reason to assume there is one. And if the B voters are actively Burying C,
>> it could be C.
>>
>> The "CD criterion" requires the system to elect C, merely to punish the B
>> voters; I think that's perverse, because, among other things, it means that
>> a system does badly with center squeeze, allowing the C faction to
>> strategize and win.
>>
>> C: No, it merely says "not B".  But CD + Plurality say that it must be C.
>>
>>
>>
>>>
>>> Since you are apparently now content to do without FBC  compliance  and
>>> you imply that electing the CW is a good thing,
>>> why don't you advocate a method that meets the Condorcet criterion?
>>>
>>> What is wrong with Smith//Approval?  Or Forest's nearly equivalent Max
>>> Covered Approval?
>>>
>>
>> Largely, it's because I think that Condorcet systems are strategically
>> counterintuitive, and hard to present results in. I think that will lead to
>> more strategy than a system like PAR. That's because PAR can make
>> guarantees that Condorcet systems can't.
>>
>> C: Such as?  What exactly does "strategically counter-intuitive" mean?
>> An example?
>>
>
> What I mean is that if you take a non-election-theorist, present an
> election scenario to them, explain who won and why, and ask how they would
> strategize in the place of voter X, they are more likely to suggest
> counterproductive strategies, and less likely to see any strategies that
> actually might work, in Condorcet than in Bucklin-like systems.
>
>
>>
>> In a system like MJ or Score, you can give a number to each candidate,
>> based on their own ratings alone, and the higher number wins. That is an
>> easy way to get monotonicity, FBC, and IIA.
>>
>> In Condorcet, no candidate has any number except in relation to all other
>> candidates. That's good for passing the Condorcet criterion (obviously) but
>> it breaks FBC and IIA.
>>
>> C:  Your method and MJ fail IIA.
>>
>
> MJ passes IIA. PAR fails it, as you say, but passes LIIA.
>
>
> Prefer Accept Reject (PAR) voting works as follows:
>
>    1. *Voters can Prefer, Accept, or Reject each candidate.* Blanks count
>    as "Reject" if no rival is explicitly rejected; otherwise, blank is
>    "Accept".
>    2. *Candidates with at least 25% Prefer, and no more than 50% reject,
>    are "viable"*. The most-preferred viable candidate (if any) is the
>    leader.
>    3. Each "prefer" is worth 1 point. For viable candidates, each
>    "accept" on a ballot which doesn't prefer the leader is also worth 1 point. *Most
>    points wins.*
>
>
>
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