[EM] What do we mean by "your vote counts"?

[Jan Kok]

Eric Gorr wrote:
>At 10:35 AM -0700 1/23/04, Jan Kok wrote:
>>Mike Ossipoff wrote (many things, including):
>>  > True, Approval doesn't let you vote all your preferences, but
>>>  at least it reliably counts all those that you vote. That can't
>>>  be said for IRV.
>>
>>What do we mean by "counts"?

>The election system would take it into account when determining the
winner.

("Takes into account" is too vague, I think...)

>IRV will never see many preferences expressed by the voters when 
>determining the winner.

>With Approval and Condorcet voting, every selection a voter makes 
>matters in determining the winner.

I'm asking for a precise definition of "counts" that people can agree
with, and then asking that people use the term consistently with the
definition.  Without a precise definition and consistent usage, it is
very hard to evaluate a claim such as Mike's, quoted above.

My straw proposal for the definition of "counts" is: "changes the
outcome of an election".


Consider a Plurality election between Jones and Smith.  According to my
definition, my vote for Smith counts ONLY IF:

the tally of all votes except mine is tied, and the tiebreaking method
would have chosen Jones if I hadn't voted

OR

the tally of all votes including mine is tied, and the tiebreaking
method chooses Smith.


If you accept that definition, then you should reject a statement such
as "With Approval and Condorcet voting, every selection a voter makes
matters in determining the winner," because in most non-tiny elections,
the outcome is not affected if any one voter votes or does not vote.


Consider an election under a method that fails FBC or monotonicity.
According to my definition, if I vote for Good, and that causes Bad to
win, whereas Good or Compromise would have won had I not voted or voted
differently, then my vote DID count - just not the way I wanted!


So what is Mike really saying here?:

>>> True, Approval doesn't let you vote all your preferences, but
>>>  at least it reliably counts all those that you vote. That can't
>>>  be said for IRV.


Obviously he is not using "counts" according to the definition I
proposed, because in most elections, no one's vote "counts".

Perhaps he means "There is a higher probability that one of your voted
preferences counts under Approval, compared with IRV."  But that leaves
open the question of exactly what probabilities are being measured,
under what conditions, etc.  Furthermore, making ones vote count is not
a desirable goal by itself, if the vote counts in the opposite direction
from what you intended.  (I may illustrate that more in a separate
post.)

So, does he mean "Every voter has a higher expected outcome under
Approval vs. IRV," or "The expected SU is higher under Approval vs.
IRV"?  Maybe, but that would be difficult to prove, I think.  And
looking at Mike's words, it seems that he trying to make a narrower
claim.

I'm still confused...
- Jan