Yesterday I posted a definition of preference, but I don`t know if it�s as complete as it should be, or a if different approach isn�t better, or even if a definition is needed.
Markus doesn�t like the mention of preference in a criterion, and implies that it�s somehow necessarily imprecise. I don�t agree. Here are a few approaches to the meaning of preference:
1. No definition needed. Some criteria definitions, and their supporting definitions for some terms in the criteria definitions, have statements that are conditional upon some voters preferring one candidate to another. Then, in an example or scenario that I write to show compliance or noncompliance with the criterion, I specify the preferences of some voters. For the purpose of the criterion, what matters if a certain preference exists, but it doesn�t matter what "prefer" actually means. So, no definition is needed.
1a. Further, one approach would be to say that not only does it not matter what preference means, but it doesn�t even matter if it means anything. After all, it�s undestood that the writer of a voting situation example or scenario intended to demonstrate something can specify anything he wants to about the example, and whatever he says is taken as true in that example or scenario. An utterance that uses a meaningless word is a meaningless utterence, and meaningless utterances aren�t statements, and aren�t true or false, but it could be argued that, since it�s understood that what the example-writer says about the voters, votes and candidates in the example is assumed true, then, if that requires that the utterance mean something, then that assumption that the utterance is a true statrement automatically contains the assumption that the utterance is a statement and means something, even if that assumption is known to be false.
So, by that approach, I could just as well speak in the criteria about whether a majority of the voters [**:_?'] candidate X to candidate Y, as long as I specify in the example that those voters [**;:_?'] X to Y.
No, I�m not a logician, so let me know if that isn�t so.
1b. But "prefer" does mean something. However imprecise that meaning is, and even if it were agreed by all that its meaning is unknown, it still means something. For that reason, that word�s use in an utterance doesn�t make it a meaningless utterance. The utterance means something, even if it isn�t known what it means. That means that the utterance can be a true or false statement, and we can assume it to be true in the example (because the example-writer says so), without my having to argue that you should also falsely assume it to mean something and be a statement. One fewer assumption needed.
2. Define it. That way we avoid 1b�s reference to a fact in the world off the paper, the fact that the verb "prefer" is used all the time and means something. By defining "preference", we avoid that, while also avoiding the need for my arguing that you should just assume that "prefer" means something, as in 1a.
A definition of "prefer":
In general, a person prefes X to Y if, given the choice between X and Y s/he would choose X instead of Y.
In particular, a voter prefers candidate X to candidate Y, for a particular office, if, given the power to appoint X or Y to the office, s/he would appoint X.
And a voter prefers proposal X to proposal Y if, given the choice of enacting or implementing X or Y, s/he would enact or implement X instead of Y.
[end of general and particular definitiions of "prefer"]
Sure, it�s difficult to verify what a person�s preferences are. Blake complained that it�s a mental state. But the writer of a hypothetical example or scenario can specify whatever he wants to about it, including what its inhabitants would choose if given the opportunity.
Inelegant, sure, and so maybe one of the other approaches is preferable. Each has its appeal and un-appeal.
3. My first definition try was my information-record definition. I liked it because it didn�t ask you to assume that a word means something, as 1a does, and it doesn�t refer to facts in the world off the paper, as 1b does, or inelegantly talk about what the example�s hypothetical voters would choose if given the opportunity, as 2 does. But it�s more awkward and less clear. And I don�t know if the definition that I posted yesterday was complete, or even the best way to go about that approach.
For now, at least, I�ll stay with 1a, 1b, and 2.
Markus, you might not like it when criteria mention that voters prefer one candidate to another, and maybe the journal authors don�t write such criteria. But those things don�t mean that it�s unclear for a criterion to mention preference. You still haven't said why you think that my criteria are unclear. Don�t assume that what�s customary is the only way to do something.
For instance, I demonstrated why Approval passes WDSC, and why margins Condorcet fails WDSC. When compliances and noncompliances can be clearly and undeniably demonstrated, then that�s the only kind of clarity that a criterion really needs. Can you name a plausible situation in which it would be difficult to say whether or not a method meets one of my criteria. No, I don�t mean a method for which a demonstration hasn�t been found. I mean a situation in which it�s debatable or could be argued either way whether or not a method meets one of my criteria.
In particular, do you find anything doubtful about my demonstrations that Approval meets WDSC and margins Condorcet fails WDSC?
Mike Ossipoff
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