[EM] PAR is awesome part 1/2: FBC?
C.Benham
cbenham at adam.com.au
Wed Nov 16 23:25:28 PST 2016
On 11/14/2016 1:48 AM, Jameson Quinn wrote:
> 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?
Jameson,
Much more than it was, thanks. In the example you give, if the ???
cohort vote A>> B=C then under PAR if the "ego" faction gives Rejects to
A then C will win
and if they give Accepts or Prefers to A then A will win.
But is there a precisely worded criterion about this "slippery slope"
problem? Is there anything non-arbitrary about the numbers you chose
for your example?
In your example there doesn't seem to be any problem if the method meets
Condorcet or is IRV.
> MJ passes IIA.
I suppose if a losing "irrelevant" candidate is removed and the number
of ballots remain unchanged and no voters react by changing any of their
ratings
of any of the remaining candidates, then I suppose it might (in a
useless and abstract way).
The claim I've seen made that it also meets some version of Majority
involves a bit of goal-post shifting.
Chris Benham
On 11/14/2016 1:48 AM, Jameson Quinn wrote:
>
>
> 2016-11-13 6:34 GMT-05:00 C.Benham <cbenham at adam.com.au
> <mailto: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
>> <mailto: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
>>> <mailto: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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