[EM] Re: Definition of fully voting one candidate over another

[MIKE OSSIPOFF]

Kevin wrote:

What is gained by using this wording, instead of just saying "A voter V
fully votes X over Y if when V is the only voter and X and Y are the
only candidates, X is the unique winner"?

I reply:

That's almost, but not quite, how I write Richard's definition of voting X 
over Y. Richard's definition was a simplification of mine, and rather 
similar to it.

You ask what's gained. What's gained is the difference between voting X over 
Y and fully voting X over Y. But let me give you an example:

Say the method is 0-100 CR. You give 100 points to X, and you give 99 points 
to Y. You're voting X over Y, by my definition, and by Richard's definition. 
But you aren't fully voting X over Y, as I've defined fully voting X over Y.

Let me tell you Richard's definition of voting X over Y, as I word it:

A voter votes X over Y if s/he votes in such a way that if we count only hir 
ballot, with everyone deleted from it but X & Y, X is the unique winner.

[end of brief definition of voting X over Y]

My definition of voting X over Y:

A voter votes X over Y if s/he votes in such a way that it's possible to 
contrive a configuration of other people's ballots such that, if all but X & 
Y are deleted from the ballot, X is the unique winner if & only if we count 
that voter's ballot.

[end of longer definition of voting X over Y]

Richard's briefer definition is the one that I usually use, because of its 
brevity. But someone could devise some unproposed or unproposable method 
whose count rules directly or indirectly require more than one voter, or 
which specifies a tie or no result when there's one voter, or gives the win 
to the candidate lower in the alphabet, or chooses randomly when there's 
just one voter. For instance, some organizations have a "quorum", a minimum 
number of participants without which business cannot be done.


That's why I still refer to the longer definition as my definition of voting 
one candidate over another.

Now, in my example, using the briefer definition of voting X over Y, to 
which your definition is similar: When you give X 100 points and Y 99 
points, and we count only your ballot, X is the unique winner. So you have 
voted X over Y.

But say there's an even number of voters, and half gives X 100 points and Y 
99 points. Does that guarantee that Y won't be the unique winner, no matter 
how the other half votes? No. The other half could give Y 100 points and X 
98 points (or zero points). Y would be the unique winner. In that CR 
example, you have voted X over Y, but you have not fully voted X over Y.

That's the difference, and that's why it's worthwhile to define fully voting 
X over Y.

You continued:

I am interested in how you define "merely voting X over Y," I believe was
the wording you used.

I reply:

I don't define "merely votintg X over Y". But I define voting X over Y, and 
most dictionaries define "merely". So I leave it to you to put those 2 
definitions together, to figure out what it means to merely vote X over Y.

In case you don't have a dictionary, to "merely" do something means to do it 
instead of and without doing something similar but more extreme, or instead 
of and without doing other things that you could be expected to do in 
connection with the a situation under discussion in the context of the 
conversation. But don't take my word for what "merely" means. I encourage 
you to look it up in a dictionary.

I said "Merely voting X over Y", because I thought that it would clarify the 
distinction from fully voting  X over Y. But if that will confuse you, then 
leave out the word "merely". Pretend that I merely said "Voting X over Y", 
instead of saying "merely voting X over Y".

You continued:

In other words I'm not sure what meaning you have
in mind with "fully."

I reply:

It isn't entirely clear what you mean by "have in mind". Do you want me to 
repeat the criterion's definition? Ok:

Definition of fully voting X over Y:

A voter fully votes X over Y if s/he votes in such a way that if there's an 
even number of voters, and half of them vote in that way, and if all 
candidates but X & Y are deleted from the ballots, then it's impossible for 
Y to be the unique winner, no matter how the other half vote.

[end of definition of fully voting X over Y]

Does that answer your question?

Mike Ossipoff

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