[EM] Remember Toby

[Juho Laatu]

On 1.6.2011, at 13.48, Kevin Venzke wrote:

> Hi Juho,

Hi,

I was busy with other activities for a while but here are some comments.

> 
> --- En date de : Mer 1.6.11, Juho Laatu <juho4880 at yahoo.co.uk> a écrit :
>>> I agree with Kevin that "elect the CW if there is one,
>> else elect the 
>>> candidate ranked (or ranked above last) on the
>> greatest number of ballots" is plenty simple, and is much 
>>> more satisfactory than MinMax or Copeland in other
>> respects.
>> 
>> In what sense is the above mentioned "implicit approval
>> cutoff" + Approval to resolve is the best "simple" method?
>> If compared to MinMax, is it maybe easier to explain to the
>> voters, more strategy free, or yields better winners? Would
>> an explicit approval cutoff be fine (to allow full rankings
>> to be given)?
> 
> It is surely easier to explain than MinMax,

If we talk about the sincere voting procedure, then MinMax voter only needs to rank candidates, but if loops are resolved using implicit Approval, then the voter should know in addition to the idea of ranking that truncation means that the remaining candidates are not approved. The voter needs to decide where to truncate. Or alternatively one could let the voters vote without knowing that truncation means disapproval. That would give more power to those that have the knowledge (although not very much if approvals are expected to come into play only seldom). I note also that if we don't tell to the voters how their ballots will be interpreted, then all Condorcet methods become very similar from the sincere voting procedure point of view (just rank the candidates sincerely and that's it).

If explanation to regular voters should contain strategic voting aspects, then the methods become more complex to the regular voter. I don't know if voters should be trained to use of approval as a tie breaker or if those properties should be hidden from the voters as discussed above. Burial would be even more difficult to explain (but maybe not recommended to the voters). In Approval all voters are expected to vote strategically (=decide where to put the cutoff), but if one uses approval only for tie breaking then one need not be as careful as with normal Approval.

If we talk about the vote counting process (with sincere votes) and how to explain it, then we have a two phase explanation (=Condorcet winner, and alternatively sum of all the ticks in the ballots if there is no Condorcet winner) vs. a one or two phase MinMax explanation (elect the candidate worst worst defeat is least bad. MinMax(margins) is quite simple since it is enough to refer to the number of additional votes each candidate would need to win all others (if doesn't already). None of the explanations is quite obvious to average voters if one has to explain the difference between having a Condorcet winner and not having a Condorcet winner. The MinMax(margins) specific explanation is maybe easiest (and still fair, clear and exact enough) to present without talking about the probabilities of having or not having a top cycle.

If we seek simplicity, I'd be happiest to explain the voting procedure simply "just rank the candidates" and use the MinMax(margins) "additional votes" explanation if the voters need to know how the votes are counted.

> has more obvious burial 
> disincentive (especially if the comparison is to margins),

All Condorcet methods have a burial incentive with some variation between different methods. I don't know why margins would be more problematic than winning votes. I mean that they have different kind of vulnerabilities and disincentives, and it is not straight forward to say which ones are more problematic. Also Condorcet with approval as a tie-breaker has its own burial problems, although the approval cutoff introduces also some risk to the burying strategy. I'll give one example of a burying strategy when approval is used for tie-breaking.

49: A>B
02: B>A
49: C

A wins. But if the two B supporters vote B>C, then there is a cycle, implicit approvals will be used, and B wins.

One possible comment to this strategy problem is that A supporters could truncate and not approve B (that seems to come from the same party or the same coalition at least). In that case all the big groupings could simply bullet vote and only the small ones would rank their second favourites. That approach could kill the chances centrists that are not the first candidates of one of the major groupings as potential compromise candidates and Condorcet winners.

It seems I have to give one more example to cover also cases where the difference between major an minor candidates is not that clear.

26: A>B
25: B>A
49: C

Again, if two of the B supporters vote B>C, then B wins. If some A and B supporters truncate in order to defend against burying or as a general safety measure against the other competing grouping (A and B supporters may not guess right which one of them will have more votes), then C wins. Before the election A and B groupings could both claim that they are bigger and therefore they should truncate, and all the voters of the other grouping should rank also the candidate of the other grouping.

This second example comes close to the traditional Approval strategy related problems where near clone parties/candidates fight about who must approve whom. The strategic problems of approval as a tie-breaker and winning votes are also quite closely related.

Although use of approval as the tie-breaker has some disincentive against burial in the sense that approving some unwanted candidate increases the risk of electing that candidate, in these examples burial works anyway. Plain Approval method is free of the burial strategy but that does not mean that this property can be carried also to Condorcet methods that use approval for tie-breaking.

> and, in my
> view, gives comparably good winners to WV,

Did you mean "when compared to WV"? The approval tie-breaker version clearly assumes an implicit approval cutoff, so in that sense it may collect more information than basic ranking based Condorcet methods. But on the other hand an implicit approval cutoff cuts away some ranking information that could have been useful. Since approvals are used only when there is a top cycle, that approach may lose more ranking information (due to truncation) than it gives additional approval information. Picking good winners would benefit of collecting lots of sincere information. (There may also be different opinions on what kind of candidates would be good winners.)

> but more attention may need to
> be placed on where to stop ranking than under WV. (In practice, I would
> not plan to rank any lower than could possibly help me in WV, so I would
> probably vote the same under both methods.)

This sounds like voters would need to use some (cutoff placing) strategy while voting. That does not make the methods simpler to the voters.

> 
> The favorite betrayal incentive is worse than WV though. (This is where
> I should plug my ICA method, which satisfies FBC. But it's more
> complicated.)

I'll skip this part since the mail is about to become so long (and this one would require more work from me :-).

> 
> An explicit approval cutoff in this method is not fine at all: You will
> lose the burial disincentive. You would be able to try to stop your
> opponents from winning as CW without hurting your own candidate's odds
> to win that way, and then in the approval count you would not have to
> stand by the pawn candidates you voted for. This strategy would only
> backfire when too many voters try it and make a pawn candidate the CW.

Yes, some of the disincentive is lost. But there are also other reasons why burial may backfire. You may not manage to create a loop and the pawn candidate might win.

If voters manage to create a cycle, the end result could be a quite sincere Approval election, i.e. not an outright victory to the ones who created the cycle (=some disincentive). In that election those voters that falsified their preferences e.g. from A>B>C to A>C>B would still have a dilemma of being forced to (explicitly) approve also C if they want to (explicitly) approve B (in addition to the obvious A) (=some disincentive).

> 
> ---
> 
> Also, the reason I don't need to see Smith in this method is that unlike
> MinMax, where there isn't an obvious justification for failing Smith,

I think there is an obvious justification for failing Smith. If one of the candidates outside the Smith set is less controversial (in terms of number of votes needed to become a Condorcet winner, or in terms of size of opposition planning to work against the elected candidate in favour of some other candidate vs. number of supporters) then why not elect that candidate. This is one very rational way of measuring which candidate should be elected. There may be other criteria too, but not necessarily any better than this one.

(Actually I think the popularity of Smith set comes partially from the temptation of forcing the circular preferences to a linear order. In that case the natural position of the top cycle may appear to be ahead of the other candidates. This approach can however be considered irrational since it completely hides away the defeats within the cycle. Forcing cyclic preferences to linear ones is thus the dangerous (and irrational) part. The opinions are cyclic and there is no need to establish a linear order. Other criteria may work better, like e.g. the the opposition against the elected candidate. Another reason behind the popularity of Smith set is the interest to make a method clone proof. That is a positive target. But it may violate other criteria, like making the least controversial candidate win. In the case of MinMax and possibility of electing outside the top cycle, violation of the clone criterion is not very critical, i.e. the number of candidates that parties nominate may not change despite of not meeting this criterion 100%.)

> in C//A the second step is a completely different method. If one doesn't
> think that Approval can justify itself, then I doubt C//A is attractive
> anyway.

I don't like Approval as a method much (because of its problems when there are more than 2 potential winners), but using approval as a tie-breaker doesn't sound as bad since then we are typically talking about cycles between three almost equal candidates in some rare cases. In typical elections traditional Condorcet methods may work well enough, so I'm not sure that all elections need additional tricks to get the properties that one wants (e.g. avoid widespread use of strategies).

Juho


> 
> Kevin
> 
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