[EM] Meaning of preference, four approaches

[MIKE OSSIPOFF]

Often when there´s something that I want to say, especially about a previous 
posting of mine, I say it before I check the new list messages. Partly so 
that what I say won´t be influenced by anything elese that has been said. 
For instance now I haven´t checked the list today yet, and maybe someone has 
objected to my definition of preference.

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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