[EM] [CES #8922] Score Voting and Approval Voting not practically substantially different from Plurality?

[Benjamin Grant]

On Mon, Jun 24, 2013 at 12:50 PM, Kevin Venzke <stepjak at yahoo.fr> wrote:

>
> >But you can change the scenario so that Plurality would be failed:
> >>
> >>51: C1 rated 5, C2 unrated
> >>
> >>49: C2 rated 10, C1 unrated
> >>
> >>Kevin
> >>
> >
> >A little confused again.  What voting system are we using above? Lost
> track of that.
>
>
> My assumption was that we were talking about Range, with blank ratings
> counting as zero.
>
> Kevin
>
>
If we are talking about Range and counting blank rating as zero, then this:

51: C1 rated 5, C2 unrated
49: C2 rated 10, C1 unrated

is really no different than this:

51: C1 rated 5, C2 rated 0
49: C2 rated 10, C1 rated 0

And I think, since plurality says ""If there are two candidates X and Y
so that X has more first place votes than Y has any place votes, then
Y shouldn't win", then X and Y have the same number of "any" place votes,
i.e., Range voting can NEVER fail plurality. Again, I can't imagine a
decent system that would.

Now if there was some functional difference between a 0 rating and no
rating at all, we could examine that, I think.  For example, I have hear
some people talking about averages, what if a lack of rating *was*
functionally different from a 0 rating?  What if the score each candidate
gets isn't the *sum* of all their ratings (with unratings = 0) but the
average of all their ratings, with a non-rating not counting against them?

Let me work this through here. According to the "sum" approach, C1 gets 5 *
51 = 255 and C2 gets 10 * 49 = 490, C2 wins.

If we are looking for the average, then C! obviously has an average of 5
among the 51 people who gave him a rating, while C2 obviously has an
average of 10. C2 wins.

It's interesting to note that whether or not you use sum or average both of
the first example above turn out the same way.

In any case, with a Range/Score system that permits people to have a
functionally different from zero "no rating" option, I still have an issue
concluding the the Plurality criterion was failed.  Did C1 have more "first
place" votes than C2? I don't think so. Therefor Plurality is not violated,
is it? Because in order for Plurality to be violated, the one candidate
would have to get more first place votes that another has ANY place votes,
and still lose. As far as I can see here, C2 had more first place votes
that C1.  Is there a way to get C1 to win while C2 has more first place
votes than C1 has ANY place votes? I cannot imagine that in this
circumstance.

Can you?

What am I missing?  Or have I screwed up somewhere?

-Benn
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