Re: [EM] A few concluding points about SFC, CC, method choice, etc.
Pasting from Mike's page: /Some definitions useful in subsequent criteria definitions:/ A voter votes X over Y if he votes in a way such that if we count only his ballot, with all the candidates but X Y deleted from it, X wins. [end of definition] Voting a preference for X over Y means voting X over Y. If a voter prefers X to Y, and votes X over Y, then he's voting a sincere preference. If he prefers X to Y and votes Y over X, he's falsifying a preference. A voter votes sincerely if he doesn't falsify a preference, and doesn't fail to vote a sincere preference that the balloting rules in use would have allowed him to vote in addition to the preferences that he actually did vote. [end of definition] Strategy-Free Criterion (SFC): /Preliminary definition: /A Condorcet winner (CW) is a candidate who, when compared separately to each one of the other candidates, is preferred to that other candidate by more voters than vice-versa. Note that this is about sincere preference, which may sometimes be different than actual voting. SFC: If no one falsifies a preference, and there's a CW, and a majority of all the voters prefer the CW to candidate Y, and vote sincerely, then Y shouldn't win. [end of definition] Michael Ossipoff wrote: Kevin and Chris posted their criteria that they incorrectly claimed equivalent to SFC. These same alternative SFCs have been posted to EM before and thoroughly discussed before. In fact, we've been all over this subject before. So why don't you point us to where in the EM archive we can find this earlier discussion? Are they in your opinion equivalent for ranked-ballot methods? Though Chris's and Kevin's criteria clearly are not equivalent to SFC, maybe someone could write a votes-only cirterion that is. First of all, what's this obsession about votes-only? Some people worry that criteria that give the appearance that we have to read voters' minds to see if they are met are not the easiest to check for. Now, quite aside from that, the efforts to write a votes-only equivalent criterion seem motivated by a desire to not say things that happen to be what I want to say. I want SFC to be about the fact that that majority, because they all prefer the CW to Y, and because there's no falsification (on a scale sufficient to change the outcome), can defeat Y by doing nothing other than voting sincerely. To say it in a way that doesn't say that wouldn't be SFC. If someone wrote such a criterion, then I'd recognize it as a _test_ for SFC compliance, but not as SFC. When I say that a method passes or fails SFC, and someone says What's that?, then I want to tell them the SFC described in the paragraph before this one, the one that relates to the CW, no need for other than sincere voting by the majority and non-falsified voting by everyone else. If I worded it like Kevin or Chris, it wouldn't be self-evident why it's desirable to meet that criterion. Someone could suggest that I use an alternative as the criterion, and save my SFC as a justification. No, I want the criterion's value to be self-evident. Well its value as something distinct from the Condorcet criterion isn't self-evident to me. If this CWY majority can't elect the CW, why do they necessarily care if Y is elected or not? And the way you've dressed this up, I can't see how it really qualifies as a strategy criterion. How are the members of this CWY majority supposed to know whether or not anyone falsifies a preference? And if they do know what are they supposed to do about it? From Steve Eppley's MAM page: /truncation resistance/ Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm: Define the sincere top set as the smallest subset of alternatives such that, for each alternative in the subset, say x, and each alternative outside the subset, say y, the number of voters who sincerely prefer x over y exceeds the number who sincerely prefer y over x. If no voter votes the reverse of any sincere preference regarding any pair of alternatives, and more than half of the voters rank some x in the sincere top set over some y outside the sincere top set, then y must not be elected. (This is a strengthening of a criterion having the same name promoted by Mike Ossipoff, whose weaker version applies only when the sincere top set contains only one alternative, a Condorcet winner.) This makes some sense as a strategy criterion, being about deterring a faction from truncating against the members of the sincere Smith set. The weaker version ascribed to you seems easier to test for. How does that version differ from your present SFC? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] A few concluding points about SFC, CC, method choice, etc.
Just to be explicit about the application of this to equal ranking. At 10:28 AM 2/15/2007, Chris Benham wrote: Pasting from Mike's page: Some definitions useful in subsequent criteria definitions: A voter votes X over Y if he votes in a way such that if we count only his ballot, with all the candidates but X Y deleted from it, X wins. [end of definition] Equal ranking of X and Y is clearly not voting X over Y. If we modify the ballot as stated and this is the only voter, it's a tie. Voting a preference for X over Y means voting X over Y. If a voter prefers X to Y, and votes X over Y, then he's voting a sincere preference. If he prefers X to Y and votes Y over X, he's falsifying a preference. Equal voting is neither voting a preference nor falsifying a preference. It is not expressing a preference. A voter votes sincerely if he doesn't falsify a preference, and doesn't fail to vote a sincere preference that the balloting rules in use would have allowed him to vote in addition to the preferences that he actually did vote. I find the application unclear. What is undefined is what it means for an election method to allow the expression of a preference. Plurality allows the expression of a preference. Unfortunately, it only allows the express of a preference for one candidate over all others. Approval allows the expression of a preference for a set of candidates over all others. If the ballot allows complete ranking and allows equal ranking, then any use of equal ranking where a preference actually exists, no matter how small, would be considered a failure to vote sincerely. While one can define terms any way one likes, it would seem inadvisable to define them in a way which flies in the face of ordinary usage. But what if a ballot does not allow complete ranking, or does not have enough rating levels to accomodate all candidates? It appears that the interpretation being used is that these methods don't satisfy SFC, but this would be because they don't satisfy the criterion even without falsification. SFC: If no one falsifies a preference, and there's a CW, and a majority of all the voters prefer the CW to candidate Y, and vote sincerely, then Y shouldn't win. [end of definition] Now, this has been about the definition of the criterion. Even if equal ranking in the presence of a sincere preference is not falsification, Approval, for example, fails SFC. Yet, I've argued, it fails SFC because it does better. It is clearer with Range: If no one falsifies a preference in Range of sufficiently high resolution, and all preferences are expressed, that is, equal rating is only used for absolute equality of rating, then Range still fails SFC, and it is easy to construct scenarios where it does so by choosing a winner who is clearly better for society and for the members of society individually, than the Condorcet winner. This is because of preference strength. If the CW is preferred, by a majority to a candidate A by a majority with a very small preference, such that, for practical purposes, these voters will be equally happy with the election of the CW or A, and a minority of voters strongly prefer A, such that they will be happy with A and seriously unhappy with the CW, it is quite clear that A should win. A makes *everyone* happy, the CW in this situation only makes a bare majority happy. Thus, we conclude, the Condorcet Criterion *must* be violated in some elections by an optimal method, and thus this theoretical optimum method must fail the criterion and others similar to it, such as the Majority Criterion and SFC. Of course, we need a definition of optimal. I've been suggesting that it should be explicit. Too often, when we consider methods by election criteria, we assume that a criterion is desirable, entirely apart from whether or not it chooses the optimum winner. It's *assumed*, very easily, that the majority choice is the optimum winner -- and therefore it is desirable to satisfy the Majority Criterion -- when this is certainly not clear enough to be reasonably an axiom. Any person or business which makes decisions failing to consider the strength of preferences will soon run into trouble Perhaps I should be more explicit about this. In considering a decision among many choices, I may consider the effect of each choice on various aspects of my life. With each aspect, I may have a preference among the choices. If we model the importance of an aspect by a number of voters voting according to that, then systems which only rank but do not consider preference strength can seriously fail to make an optimum decision. The additional necessary element is to incorporate preference strength. Decision-making strategies often use this, quite explicitly. One will give weight to various aspects of a decision, and for each aspect a numerical rating can be used. Then, for each choice, the rating is multiplied by the weight and the
[EM] A few concluding points about SFC, CC, method choice, etc.
Kevin and Chris posted their criteria that they incorrectly claimed equivalent to SFC. These same alternative SFCs have been posted to EM before and thoroughly discussed before. In fact, we've been all over this subject before. Though Chris's and Kevin's criteria clearly are not equivalent to SFC, maybe someone could write a votes-only cirterion that is. First of all, what's this obsession about votes-only? Though my IIAC is votes-only, everyone invokes a preference-based IIAC (though no one defines it). The Condorcet Winner (CW) is defined in a preference-based way. Anyway, maybe someone could write a votes-only criterion equivalent to SFC. It would be an inelegant, arbitrary, grafted hodgepodge. As I said, weve been over this. For instance, since no nonrank method can meet SFC anyway, someone could stipulate, in their criterions premise or requirement, that the method being tested be a rank method. If the stipulation is in the premise, then the criterion applies only to rank methods. It wont rate Condorcet better than Plurality, but I will compare Condorcet to IRV or Borda or Dodgson or Copeland. Im not saying that wouldnt be of any use at all, to compare the rank methods, but my criteria apply to and compare all the methods. If the stipulation is in the criterions requirement, then it arbitrarily and dictatorially says that nonrank methods fail the criterion. Now it applies to all methods. But not in the seamless way that my criteria apply to all methods. You must agree that theres something a little Worthless-sounding about a criterion that says Nonrank methods fail this criterion because I say so. So, even if someone could write a vctes-only SFC-equivalent, it would be offensive to me, for the above reasons, and I wouldnt use it. Now, quite aside from that, the efforts to write a votes-only equivalent criterion seem motivated by a desire to not say things that happen to be what I want to say. I want SFC to be about the fact that that majority, because they all prefer the CW to Y, and because theres no falsification (on a scale sufficient to change the outcome), can defeat Y by doing nothing other than voting sincerely. To say it in a way that doesnt say that wouldnt be SFC. If someone wrote such a criterion, then Id recognize it as a _test_ for SFC compliance, but not as SFC. When I say that a method passes or fails SFC, and someone says Whats that?, then I want to tell them the SFC described in the paragraph before this one, the one that relates to the CW, no need for other than sincere voting by the majority and non-falsified voting by everyone else. If I worded it like Kevin or Chris, it wouldnt be self-evident why its desirable to meet that criterion. Someone could suggest that I use an alternative as the criterion, and save my SFC as a justification. No, I want the criterions value to be self-evident. As I said, some more convenient equivalent could be used as a test, but not as the main definition, the one that is offered or featured. The same could be said for my other defensive strategy criteria. There are 5 of them: FBC, SFC, GSFC, WDSC and SDSC. The latter four are the majority defensive strategy criteria. As I said (buried in a long reply), the defensive strategy criteria are what I have to say about single-winner voting systems. So, regarding SSD vs. RV, what I have to say is: SFC,. GSFC, SDSC. Another thing: This issue about ways of defining a criterion isnt only about my defensive strategy criteria. It applies likewise to popular criteria. Of my defensive strategy criteria, only FBC has any popularity. For instance, the issue applies to Condocets Criterion, which, I claim (and have long claimed) is nonsense as its usually defined. In some versions it applies only to rank methods. In some versions it arbitrarily stipulates that only rank methods pass it. My own wording of CC is the only one that is any good. Some people have expressed discomfort with a criterion that mentions preference (but the same people dont seem to have a problem with a preference-based IIAC (though Im not aware of one that is actually defined). A few years ago I posted to EM a precise abstract definition of preference. But I also told why no definition of it is needed. None is needed because, whatever you think prefer means, it means the same thing whenever used, in the criterion and in the statement of a failure example. It therefore doesnt matter if prefer means anything at all. One could instead use some fanciful made-up verb from Lewis Carroll, such as outgribe (which Carroll uses only in its strong-irregular past tense, outgrabe. Much better people than Warren have tried to find fault with the defensive strategy criteria. Theyre battle-tested. Mike Ossipoff election-methods mailing list - see http://electorama.com/em for list info
