Condorcet's mathematical built-in bias

[Mike Ossipoff]

donald at mich.com writes:

Mike says: So much for my promise. Even if the silliest garbage
isn't answered, it's going to look to some as if it wasn't
answered because it was irrefutable. 

One solution would be if there were a declaration, not by 1 person,
but by several, all of the people whom Don is slinging this
garbage at, that none of them would answer him. If it were
_official_ that, even though (for some inexplicable reason) Don
is still on these lists, he won't be answered by the people
he's been wasting the time of all these months.

That would be the easiest solution, not requiring any technological
fixes, and would also save Steve, Rob, & Demorep some time too.

Another solution would be for any 1 particular person who doesn't
want to continue with this silliness to be able to not receive
any of Don's postings. Since my mailer can't do that, & my
Internet service can't do it, can the EM & ER listservers by
adjusted to avoid sending a certain person's postings to a certain
other person? But the feature would have to be sophisticated enough
to also not send me things _replying to_ Dons outpourings. That
may be asking too much of the technology.

What I can say for sure is that 1 of these solutions mentioned
here is necessary. Have you ever had the experience where a
baby in a highchair starts throwing a toy onto the floor, and you
pick it up & put it back on the highchair tray? And the baby
makes a game out of it, throwing it back off the tray every time
you replace it on the tray? That's what we're doing here. It's
easy for Don to sloppily, carelessly churn out these nonsensical
letters, like the one I'm replying to here. I don't know about
you, but I'm tired of babysitting Don. That's become pretty
much the entire business of this list, and, as far as sw methods
are concerned, that's what's happening on ER too.

I'm not into keeping this up. In addition to the solutions
mentioned earlier in this letter (Officially stated policy
by those with whom Don is arguing, not to answer him; filteringg
Don's letters (& their replies) from me (or whoever else requests
it)--there remains the solution that I'm not supposed to talk
about. Well, if I suggest removing the joker from these lists,
and I get kicked off of them as a result, that's a solution too,
isn't it.

In any case, this situation isn't acceptable.

***

Anyway, now to reply to the latest installment:

> 
> Greetings Methods list,
> 
> DEMOREP1 wrote:
> Thus, there can be a compromise candidate (such as M) who beats each other
> candidate in all of his/her head to head pairings.
> Can IRO fans comprehend such compromise candidate possibility ?
> 
> Donald writes:
> Not so fast DEMOREP1 - your success of the so called compromise candidate
> depend in part on built-in mathematical bias.
> 
> Condorcet's pairing has a mathematical built-in bias that favors the low
> candidate. On the first selection all candidates have a mathematical equal
> chance at receiving votes. Each are free to receive between zero to one
> hundred percent of the votes. But on the second and further selections
> there is a bias that favors the low candidate of the first selection. On
> the average the low candidate will receive more votes on the second
> selection than the other candidates. Consider this example:

So what? How does it favor him to have 2nd choice positions instead
of 1st choice? Those people who have ranked Middle over Extreme1,
if those people had, instead, all ranked Middle 1st (giving
him an outright 1st choice majority), is Middle somehow less
"favored" by that? That's what you're saying when you say he's
favored by not being ranked 1st, because he gets to be ranked
2nd (?) :-)

But your claim that ranking someone lower can make them more
likely to win is especially ironic, because IRO is famous
for being like that. It's called "nonmonotonicity". IRO
is nonmonotonic. Condorcet isn't. In fact, I don't know of
any methods other than elimination methods that are nonmonotonic.
IRO is, so far as I've heard, the only nonmonotonic method
being proposed publicly, on these lists or elsewhere.

> 
>               (  ) A            (  ) B          (  ) C
>               (  ) AB           (  ) BA         (  ) CA
>               (  ) AC           (  ) BC         (  ) CB
>              --------          --------        --------
>                49  A             41  B           10  C
> 
> Now - if one hundred people were to fill in the amounts, at random, that I
> have left vacant so that the final totals will be  49 A  41 B  10 C  we
> will find that on the average candidate C is going to receive more votes in
> the second column of selections because C has more possible second

Which, of course makes C better off than if he had gotten more
1st choice votes :-)

> selections chances - 90 possible vote selections for C vs 59 for A and 51
> for B. This is a built-in mathematical bias. Candidate C cannot help but to
> gain more - no place to go but up.

I can just hear candidates asking their supporters to not vote
them 1st place, so that, being at the bottom, they'll have nowhere
to go but up  :-)

> 
> Candidate C may have been the lowest on the first tally but as each
> selection is used candidate C will be closing the gap with the others.
> Condorcet's bias is part of the reason when pairwise selects the last
> candidate to be the winner.

The last candidate according to your reckoning by 1st choice vote-
count. If you start with the premise that 1st choice votes is
the thing to go by, then predictably IRO will look best. As I
keep telling you, it depends on the dessired-ness of the standard
that you're going by. You keep simply assuming that 1st choice
vote-count is the thing to go by. Now it's evident that you aren't
being coy this time, & that you really believe your hippo logic.

> 
> Another way to see this is as follows: Suppose there was a plurality
> election in which no candidate received a majority and the election boss
> told the voters: "We have no winner so you people are required to vote
> again but this time you cannot vote for the same candidate - you must vote
> for some other candidate."

This, of course has no resemblence to Condorcet's method, and 
so your mention of it has no relevance.

> Well - under these conditions the low candidate cannot help but get more
> votes than he got in the first election - maybe even enough to win - but
> running elections like this is absurded - like Condorcet is absurded.
> 
> It is improper to add second selections to first selections - Condorcet is
> improper.

And you, Don, are the arbiter of what's proper. :-) I prefer to go
by widely held basic standards & principles. You're right only
if you are accepted as the ultimate judge of what's proper.

> 
> The voters of the last candidate are in the position of deciding which of
> the two leading candidates will be the winner - but they and you have no
> right to assume that the low cndidate should be the winner.

No one has a right to choose as winner the candidate that Don
says shouldn't win, the candidate who is lowest by Don's standard,
Plurality.

> 
> Donald,

Enough of this. Which of those solutions is the most feasible, or
the most acceptable to the 2 list-owners?

The list owners can, of course decide, or, if they wanted to,
they could call for a rank-balloting vote among the 4 alternatives
that I named in this letter.

1. The people with whom Don is arguing officially state a 
   policy of not replying to him on this issue.

2. The list owners filter Don, & the replies to him, from
   anyone who requests it.

3. Don is removed from the list.

4. Mike is removed from the list. (the default option)

***

As I said, I have nothing against the list owners choosing
an option, or calling for a rank-balloting vote.

***

Mike

> 
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> 
> .-
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