[EM] Bill: Re: our criteria & definitions

[MIKE OSSIPOFF]

Bill--

I'm still reading the new list e-mail, and probably won't get a chance to 
attack it (figuratively) tonight. So I'll do so tomorrow. But it's important 
that I reply to this matter about our definitions at the website.

You wrote:

[ Quoting from http://www.electionmethods.org/evaluation.htm ]

>In Approval Voting, a candidate is "voted higher" by being "approved"
>rather than "disapproved."

My definition of Approval is:

Each voter may mark as many candidates' names as s/he wishes to. The 
candidate receiving the most marks from voters wins.

[end of Approval definition]

Richard's definition of voting X over Y:

A ballot votes X over Y if:

If we count only that ballot, with everyone but X & Y deleted from it, then 
X is the unique winner.

[end of definition of voting X over Y]

My longer definition is sometimes useful, but that briefer definition is 
usually more convenient.

>If one candidate is preferred over each of the other candidates, that
>candidate is the Ideal Democratic Winner (IDW).

I reply:

I'll have to check the website, but that definition should be accompanied by 
a definition of "preferred over":

X is "preferred over" Y if more voters prefer X to Y than prefer Y to X.

(We're using "prefer" in the standard sense: Someone prefers X to Y if s/he 
would rather have X win than have Y win. "Preferred over" isn't about 
votes).

[end of definition of "preferred over"]

When that definitiion of "preferred over" is added, the IDW definition that 
you quoted is complete.
IDW stands for what is usually referred to as the CW.

>Condorcet Criterion (CC)
>If all votes are sincere, the Ideal Democratic Winner should win if
>one exists.

Under Approval, if one candidate is preferred / voted higher / approved
more than each of the other candidates, then that candidate will win.

I reply:

But "preferred over" isn't about votes. If the website doesn't have the 
definition of "preferred over" that I stated above, then I'm sorry for the 
omission, and we'll immediately fix it.

Our website is a committee project, and, like any committee project, no one 
participant can get everything worded exactly as they'd like to. My wording 
goal is precision. Russ sometimes says that I go too far in legal-like 
wording to make things precise, that the precise wording can be awkward, and 
so he sometimes simplifies the wording for clarity and smoothness.

Or sometimes I want to define a word, but Russ feels that the reader's 
understanding of that word's meaning is already probably good enough. For 
instance, the website probably doesn't state the definition of voting X over 
Y.

Sometimes neatening-up can remove a definition that I consider important. If 
that has happened, and that's why "preferred over" isn't defined at the 
website, that will be fixed immediately.

So, for a candidate to be the IDW merely means that, when compared separatly 
to each one of the others, s/he is preferred to him/her by more voters than 
vice-versa. (Where "preferred" is used in the usual sense meaning that 
someone prefers X to Y if s/he would rather have X win than have Y win).

So then, the IDW doesn't necessarily win in Approval.

You continued:

Therefore Approval meets CC.

I reply:

Approval doesn't meet our CC. But Approval & Plurality meet Blake Cretney's 
CC. Or they would except that Blake avoids that by stipulating that CC 
applies only to rank methods. Our CC applies meaningfully and as-expected to 
all methods. Check Markus's CC. If Markus defines CC, most likely Plurality 
passes Markus's CC too, unless Markus copies Blake's stipulation that CC 
applies only to rank methods.

I assume that this quote is from our website:

>Non-ranking methods such as Plurality and Approval could not possibly
>comply with the Condorcet Criterion because they do not allow each
>voter to fully specify their preferences.

You said:

CC doesn't say anything about requiring "fully specified" preferences.

I reply:

No, our CC doesn't lexicographically require that, but it's still true that 
Approval & Plurality don't meet CC because they don't allow the voter to 
vote every one of his/her sincere pairwise prefrences. The reason for this 
disagreement will be clarified below:

You said:

"Preferred" and "voted higher" mean the same thing, under any reasonable
interpretation.

I reply:

...but not by the dictionary definiton of "prefer". Sometimes dictionary 
definitions aren't precise enough, but even then our usage should be based 
on the dictionary meaning as nearly as possible.

And if we didn't define "prefer", the ordinarily-accepted meaning should be 
the default meaning.
When people say they prefer one outcome to another, they mean that they're 
rather have that outcome than the other, not that they have voted for one 
over the other.

But yes, I agree that unclarified interchangeability of "prefer to" & "vote 
over" are the kind of things that you'll probably find at Blake's website.

Are you sure that it's unreasonable to say that  "prefer" and "vote higher" 
aren't the same?

Say Kucinich wins the nomination. Say Nader runs too.
Say you would rather have Nader win than have Kucinich win. But you feel 
that Kucinich has a better chance, and so you vote for Kucinich in 
Plurality. You prefer Nader to Kucinich, but you vote Kucinich over Nader.

I suggest that the most reasonable definition of prefer is its dictionary 
definition, which is about wanting one outcome more than another. That 
dictionary definition of "prefer" is different from the meaning of voting 
one candidate over another. I don't know if you'll find a dictionary that 
has several mutually conflicting definitions of "prefer". So I repeat that 
in accepted usage, you prefer one outcome to another if you'd rather have 
that outcome than the other.

I haven't checked those definitions lately, at the website, but if we use 
"prefer" we should clarify that we mean its standard meaning of wanting one 
outcome more than another. But even if the website doesn't have that 
definition, it isn't reasonable to assume that "prefer" has come to mean the 
same as "vote over".

Now, about your earlier statement:

Our CC definition stipulates sincere voting by everyone. Our website defines 
sincere voting as:

A voter votes sincerely if s/he doesn't falsify a preference, or fail to 
vote a preference that the balloting system in use would have allowed 
him/her to vote in addition to the preferences that s/he actually did vote.

[end of sincere voting definition]

I've probably posted the definitions of falsifying a preference and voting a 
preference. I don't know if those definitions are at the website. I'd 
"prefer" that they be there.

So, if rank balloting is used, and you can rank as many as you want, then 
your ballot is sincere onlly if you rank all the candidates. So, though our 
CC doesn't lexicographically require voting all of one's preferences, it 
does require sincere voting, and sincere voting, when rank balloting is 
used, requires voting all of one's pairwise preferences--because rank 
balloting allows it.

I hope that clears up that objection.

With Plurality, the only sincere vote is for one's favorite--otherwise 
you're falsifying a preference.

So if your favorite isn't the CW, then you aren't voting the CW over anyone 
in sincere Plurality voting.

You might not agree with our definition of sincere voting, but you can't say 
that we didn't post it at the website. Our sincerity definition is 
convenient: It specifies something that is meaningful in the definitions of 
criteria. And it's a reasonable definition too. If you falsify a preference 
that's obviously insincere. But if you avoidably refuse to vote a 
preference, that could be called less than sincere too. We call it insincere 
to not vote a preference if the balloting system in use would allow you to 
vote that preference in addition to the preferences that you actually did 
vote.

I claim that sincerity definition makes sense, as an especially demanding 
definition of sincerity. Maybe a llittle too demanding you might say. Ok, 
but it's needed for the criteria to say what we want them to say.

You continued:

If Approval satisfies MC, it also satisfies CC.

I reply:

Maybe at Blake's website.

We define CC in terms of sincere voting and sincere preferences (since the 
CW is defined in terms of sincere preferences). Pretty much everyone defines 
MC in terms of voted preferences. MC is understood to be about actual votes, 
and so I don't disagree with defining MC in that way. It seems to me that 
it's widely agreed that Plurality meets MC. So Approval meets MC but fails 
our CC. However, in lots of academic definitions, MC will be defined in 
terms of "preference", but Markus once posted that in academic usage 
"preference" means "voted preference". Blake might have copied that usage 
into his website. I haven't checked lately.

Likewise, most definitions of the Pareto criterion say that a candidate 
shouldn't win if someone else is preferred to him by everyone. I assume that 
they mean "voted over him", though those definitions of Pareto aren't 
accompanied by a definition of "prefer", much less "vote over".

You might prefer Nader to Kucinich, but vote Kucinich over Nader.

The academics tend to be vague about things like that.
I try to avoid that vagueness. I'll re-check the website again, and if it 
isn't defining everything that needs to be defined, then I'll urge that we 
put up all the definitions that are needed.

Mike Ossipoff

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