Thanks for feedback. I will address as many points as I can tonight, but I will have to get back later with revised versions of the first four criteria.
-- Richard
Mike wrote:
Richard continued:
Here are my "votes-only" definitions:
SFC: If X beats all other candidates in pairwise comparisons, and a majority of ballots rank X over Y, then Y does not win.
I reply:
If, as seems to be the case, based on how it's written, that criterion applies only to rank methods, then, for that reason, it isn't equivalent to SFC.
It should probably include a clause, "The method allows full ranking of all candidates, and [insert remainder of criterion here]". But first I need to ascertain that *only* methods that allow full ranking can pass the criterion. And if not, then the issue needs to be dealt with some other way (I have an idea how, but would rather have the simplest fix necessary). There may be some other changes necessary since I overlooked the impact of one of the clauses in the original definition; I'll have to give it a closer look and rewrite it. The same applies to the votes-only GSFC, WDSC, and SDSC.
Richard continued:
Note: The statement in the electionmethods.org commentary that "Compliance with SDSC means that a majority never needs any more than truncation strategy to defeat a particular candidate" is puzzling (truncation strategy is "falsely voting two candidates equal", is it not?).
I reply:
No it is not. If you don't include certain candidates in your ranking, then you aren't voting for them. If you aren't voting for them, then there isn't a compelling case that you're voting them any way, including equal. You're leaving them out equally.
So you want readers to infer something (that truncation isn't the same as "voting candidates equal") that isn't implied in the definitions?
Consider this statement, from the same web page: "In order to understand SFC, one must also understand that there are two types of insincere votes: false preferences and truncated preferences. Voters truncate by terminating their rank list before their true preferences are fully specified (note that the last choice is always implied, so leaving it out is not considered truncation). Voters falsify their preferences, on the other hand, by reversing the order of their true preferences or by specifying a preference they don't really have." We can infer from this that (1) truncated preferences are not false preferences, since they have their own separate category; and (2) "voting two candidates equal" is not a case of a falsifying preference, since it is not enumerated in that category. That leaves wide open the interpretation that truncation is the same as "voting candidates equal", as long as we are not provided with a special definition of "voting candidates equal" such as the one you now suggest:
A voter votes X equal to Y if s/he doesn't vote X over Y, and doesn't vote Y over X, and votes X over someone, and votes Y over someone.
[end of definition of voting X over Y]
So in my next try at a votes-only definition I will have to take into account your new supporting definition.
Richard continued:
Also, the statements in the commentary about "countering offensive order reversal" are completely irrelevant, since the need for defensive strategy is based on the opposing votes cast regardless of whether those votes are the result of offensive order reversal.
I reply:
It isn't quite clear why Richard thinks that the fact that the fact that sincere votes can have the same effect as similarly voted strategic votes means that it's irrelevant to speak of countering offensive order-reversal.
Is it meaningless to speak of blocking an intentional punch because someone could also hit you accidentally, and that would be blocked too, by the same block?
To quote the web page once again:
"Compliance with SDSC means that a majority never needs any more than truncation strategy to defeat a particular candidate, even when countering offensive order reversal by that candidate's voters."
"Even when" is typically used in English as an indicator that there is a potential (in this case, for the need to apply "more than truncation strategy") that exists in the presence of the stated condition but not in its absence. But that isn't true; that is what I was getting at. The sentence retains its meaning without the misleading "even when" clause.
Richard continued:
FBC: For some set S of ballots, if R is the set of results that can occur when ballot B is added to S if candidate X is given the highest ranking on B, and R' is the set of results that can occur if ballot B is added to S when candidate X is not given the highest ranking on B, then either X is a member of R, or R' is a subset of R.
I reply:
I asked how a votes-only FBC equivalent could be written. Your criterion may or may not be equivalent to FBC. From your other criteria in your posting, I'd say the likelihood isn't promising.
It *is* FBC (with the necessary changes -- since as you pointed out these criteria must apply to more than ranked methods -- from "is given the highest ranking" to "is not voted lower than any other candidate", and from "not given the highest ranking" to "is voted lower than some other candidate". But don't take my word for it; study it carefully and try to find some way in which it's not equivalent.
In any case, FBC is written in a way that clearly, directly & obvioiusly speaks to a voter concern.
Why would anyone want to write it as Richard has written here (even if Richard's criterion is equivalent to FBC)?
I wrote it in a way that would be mathematically useful, as a point of discussion, rather than for promotional purposes. Promotion of FBC is getting off of the topic; however, I'll paraphrase it without the mathematical language, in a form very similar to the existing language: "By voting another candidate over candidate X, a voter should never get a result that he could not get without doing so, unless he could get X as the winner without doing so."
The above "FBC" wouldn't be publicly usable. If I tried, everyone would tell me they have no idea what it's supposed to mean. And even for someone who knows what it means, it doesn't speak directly, obviously and clearly to voter concerns as my own version of FBC does.
So, even if it should turn out that Richard's "FBC" is equivalent to FBC, I wouldn't adopt it or replace FBC with it.
A strange criticism, coming from the person who wrote just yesterday, "And If FBC can be written votes-only, that would help its acceptance."
-- Richard
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