accounts at museworld.com
Sun Mar 25 15:36:24 PDT 2018
Hi Juho, thank you for this example ballot set. I have added it to the codebase as a test case with some documentation. (Both Smith and Schwartz should identify A, B, and C.)
A, B, and C all defeat each other 66:33. And they each defeat d 50:49. I understand the urge to award d the win, given those numbers. But I believe that that urge ascribes “intensity of preference” to A, B, and C - when for Condorcet, which is purely ordinal, we have no idea. If I imagine those voters as voting stoically, dispassionately, poker-face, then I have no idea whether they passionately prefer A to B, or if, for instance, they are completely torn but have some consistent but trivial reason to pick one over the other. So in the absence of intensity-of-preference data, we really don’t have enough data to conclude that d should be the winner - for all we know, there actually is more passion in those 50:49 splits.
So I am having trouble seeing it as a flaw with the Smith Set concept itself. I do agree that it points to some sort of flaw, but I think the proper identification of the flaw’s home requires zooming out and looking at the framework.
Each time we step close to determining an election winner, we make a choice to lose fidelity in some fashion.
1. We have a need to collectively decide something, and so we voice that need by identifying a question to answer. But in identifying or voicing that question, we risk losing some essential part of the real question. In other words, we risk a failure of specification. But, we need to move forward, so we accept that risk, and move forward with the question as asked.
2. In asking the question, we identify options for a solution - the candidates in an election. But in doing so, we risk omitting some of the proper solution spectrum. The collected candidates may still be insufficient in some way. But, we have to draw the line somewhere, so voters are restricted to choosing between a potentially imperfect slate of candidates.
3. We set a time to choose. But in doing so, we risk the deadline being too soon for some voters, in that they might not be finished with their decision process. So we lose some fidelity there in measuring voter preference exactly.
4. We want to protect against bullying, intimidation, and some people being convinced to make their vote count “less” than someone else’s, and so we decide to protect the ideal of “one person, one vote” where every person’s vote counts the same. But there we lose some fidelity in measuring intensity of preference among voters.
So I’m inclined to think that the example below is more about the costs associated with something like #4 above. In fact, the scenario seems very similar to me, to the one I sketched out earlier - if, in a two-candidate election, A defeats B 50:49, but A’s support is lukewarm and B’s is passionate, should B win? I think you can defend that if you value “social utility” and “intensity of preference” more than “one-person-one-vote” or "majority", but I wouldn’t count that as a flaw with the Condorcet method in particular, since it’s a majority-type of voting method.
> On Mar 25, 2018, at 7:05 AM, Juho Laatu <juho.laatu at gmail.com> wrote:
>> On 25 Mar 2018, at 06:30, Curt <accounts at museworld.com> wrote:
>> What do you believe the Smith Set signifies? Is it meaningless to you other than something from which a winner should be algorithmically selected?
> To me Smith Set is a criterion that in some sense and at first sight looks natural, but on second thought does not cover all possible scenarios well. I mean that if there is a group of candidates that are a unified group, and they beat all others, then yes, one of them should at least in most cases win. This is related to clones. If all the Smith Set candidates can be considered to be clones, then nominating only one of them would probably lead to electing that candidate as a Condorcet Winner.
> What are the problems then? One problem is that those Condorcet methods that are based on rankings only, and possibly a pairwise matrix only, can carry only limited information on what the preferences of the voters are. There can be multiple explanations to what the voter preferences might have been. There are scenarios where electing from the Smith Set may not be natural.
> Another problem of the Smith Set is that it may look more natural than it is, when one draws the end results (in paper or in one's mind) so that all the Smith Set candidates are at top, and all others below. This drawing technique to some extent hides the defeats within the Smith Set from the eye.
> The best I can do to demonstrate these problems is to give you one particular (old) example scenario where selecting the winner outside of the Smith Set seems quite natural. In some extreme situations Smith Set may thus not be the right choice.
> 17: A > B > d > C
> 16: A > d > B > C
> 17: B > C > d > A
> 16: B > d > C > A
> 17: C > A > d > B
> 16: C > d > A > B
> This example is a classic strong cycle of A, B and C, with one more candidate (d) added. Candidates A, B and C are not clones since they are not next to each others in the ballots. Candidate d is not in the Smith Set, but is very close to being a Condorcet Winner (2 votes short). Candidates A, B and C are very far from being Condorcet Winners.
> BR, Juho
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