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

C.Benham cbenham at adam.com.au
Mon Nov 14 21:57:37 PST 2016


On 11/14/2016 1:48 AM, Jameson Quinn wrote:

> 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?

Jameson,

Maybe not entirely. When you refer to a "small amount" of "offensive" or 
"defensive" strategy, presumably you are talking about some members of a 
faction
voting one way and the rest another. Is that right?

I can see the problem in Approval, but under Smith//Approval in your 
scenario A is simply the CW and the "ego faction" can't do anything to 
get a result they prefer.

I'm not sure that this problem is entirely avoided in PAR. Presumably 
the C faction gives Rejects to both A and B.  If six or more of the ego 
faction give B a Reject
and six or more of the ??? faction give B an Accept then both A and C 
will be eliminated leaving B the winner.

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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