[EM] Kristofer and Steve on IRVa vs. MAM

[steve bosworth]

This reply to Kristofer's post is strengthened by the attachments it mentions and which Steve will also sent to you by email if you wish (stevebosworth at hotmail.com).

________________________________________
From: steve bosworth <stevebosworth at hotmail.com>
Sent: Sunday, May 29, 2016 7:54 PM
To: Kristofer Munsterhjelm
Subject: Re: Your 5th APR dialogue with Steve

To Kristofer,

Thank you for your response.  In one sense, I accept that if truncated ballots are not permitted, Condorcet will also support the winner with at least by 50% + 1, e.g. the MAM winner will be supported by at least 50%+1 of all the voters.  However, this ‘support’ will usually be composed mainly of indirect or ‘transitive’ support.  In contrast to IRVa, the percentage of voters who have expressly preferred the winner over each of the other candidates can easily be much less than 50%.  This is illustrated by the example discussed in the Endnote to the attached newly drafted Appendix 4 to my article (Super Equality for Each Citizen’s Vote in the Legislature’).

In that extreme example, ‘as a result of using IRV, candidate F is elected with a 61% majority and with an average intensity of preference of 9.62 out of 10.  In contrast, by counting the same 100 ballots using MAM, candidate E is elected with the explicit support of only 39% and with an average intensity of preference of 9.28.’
As a result, the attached appendix also claims that only ‘IRVa allows each citizen to guarantee:
1)      that her vote will continue quantitatively to count equally,
2)      that the winner will be elected by a majority of all the voters who have not deliberately cancelled the possibility of their otherwise wasted ‘default vote’ being counted until the majority winner is discovered, and
3)      that the winner will be supported more enthusiastically than any other candidate.’

This extract and the other passages that I see as being relevant to our discuss are printed green in the attachment.
Below, I have attempted to respond to each of the points made in your most recent email.

I understand that you may not have the time to answer until July.

Best regards,
Steve
________________________________________
From: Kristofer Munsterhjelm <km_elmet at t-online.de>
Sent: Friday, May 13, 2016 8:33 AM
To: steve bosworth
Subject: Re: Your APR dialogue with Steve, a short addition

On 04/29/2016 11:20 PM, steve bosworth wrote:

> S:  Appendix 4 also criticizes Condorcet both for not guaranteeing that
> the elected candidate is supported by at least 50% + 1 of the voters,

K:  If candidate X is the Condorcet winner, there always exists an
elimination order (i.e. "first eliminate Y, then eliminate Z, then
eliminate W") so that X ends up being supported by 50% + 1 at the end*.

Or, more generally: unless X is the Condorcet loser, there exists such
an order.
S:  Yes, but the winner at the top of this order may not have been expressly preferred by even a plurality of the voters (as illustrated by the attached Endnote).  This contrasts with the IRVa winner.
K:  However, this elimination order doesn't need to be (and often isn't) elimination in order of Plurality losers.
S:  I see no reason to disagree with this.
[….]
S: > … and for not allowing a voter’s different intensities of preference to
> affect which candidate is elected. Each of the highest, high, medium,
> low, and lowest preferences the winner has received counts the same.  This
> makes it much less probable that the winner will be as enthusiastically
> supported (on the average) by her electorate than an IRVawc or APR
> winner will be.
K:  Take a more indirect look. As far as I understand you, you mean that for
say,
1: A>B>C>D>E>F (vote a)
the A>F vote counts as much as in
1: A>F>B>C>D>E (vote b)
S: Yes.
K:  but you'd like it to count more when A and F are further apart because
that shows that the voter dislikes F more.
S: Yes.
K:  But in the Condorcet matrix,
one A>...>F vote counts the same as a direct A>F>... vote as far as the
contest between A and F is concerned, so the method doesn't seem to take
intensity into account.
S: Yes, and that is the problem.
K: However, in vote a, the voter says "I'm willing to get B, C, D, or E
before I get F".
S:  Yes.
K: What this does is increment the scores B>F, C>F, D>F,
E>F. So there *is*, in a sense, a difference of preference. By
supporting many candidates over F, the voter lessens the chance that F
will win. Suppose, for instance, that B and F were nearly tied. In vote
a, the voter does a lot more to raise B over F (to make B stronger than
F) then he does in vote b.
S: Yes, if I understand you, this ‘incrementation’ can cause each citizen’s vote to have a different value in the whole process.  If so, the principle of ‘one-citizen-one-vote’ is violated.
K:  So the voter's enthusiasm does have an effect by making more candidates
stronger before the candidate he dislikes becomes stronger. He doesn't
support A directly, but he supports a lot more of F's rivals.
S: Yes, the presence or absence of different numbers of these different ‘effects’ can result in giving some voters more weight in determining the order than other voters.  Again, this would seem to violate the principle of ‘one-citizen-one-vote’.
K:  The same argument goes for raising. When a voter goes from

1: A>B>C>D
to
1: C>A>B>D

he helps C more by protecting C from A and B, i.e. by increasing A>C and
A>B.
S: I do not understand your phrase:  ‘i.e. by increasing A>C and A>B’.  This is because C>A>B>D favors C over A.
K: If that's not enough, consider Borda-elimination. It's like IRV, except
you count by Borda score rather than by first preferences when you
decide whom to eliminate. I imagine it'll be hard to say that
Borda-elimination fails to take enthusiasm into account, because
1: A>B>C>D>E>F
gives F 0 points and A 5 points in some given round, whereas
1: A>F>B>C>D>E
gives F 4 points and A 5 points.
Yet Borda-elimination passes Condorcet. It always elects the CW when it
exists. (Thus it also produces an elimination order where the Condorcet
winner ends up being supported by 50%+1)
S: Similar to Condorcet (MAM), and in contrast to IRVa, Borda splits each citizen’s one vote between the candidates.  Consequently, some citizens will be helping to defeat their most favored candidate by the lower scores they have given to the winning candidate.  Again, the winner may not be support by 50% +1 of the full value of each vote given by each citizen.  Nor is the average intensity of support given to the Borda winner likely to be as high as the winner discovered by IRVa.
S: > Lastly, unlike IRVawc and APR, each voter’s one vote in
> Condorcet (e.g. MAM) will not have an equal effect on the distribution of voting
> power in the legislature, i.e. again,  it does not guarantee
> ‘one-citizen-one-vote’ in the assembly, e.g. some votes will be at least partly wasted.

K: IRV is nonmonotonic. That means that ranking someone higher may bump
them off the legislature, and whether that happens is unpredictable. How
can you then say that each voter's vote counts the same? It may
unpredictably count for a lot less - or more - in deciding whether
someone will get a seat.
S:  Using IRVa in the example in the attached Endnote, and when also used in your following example, each vote continues to count (directly or indirectly) as one until a majority winner is discovered.
----
K: * That is, unless there are truncated ballots, but then IRV doesn't give
a majority either.
S:  This is why I added ‘Asset Voting’ to IRV, to produce IRVa.  It seems to me that all ranking ballots should avoid truncation simply by interpreting each candidate not marked as having been rank equal bottom, except the candidates expressly ranked.
K:  E.g. single winner:

1: A
1: B
1: C
...
1: X
2: Z

Everyone but Z are eventually eliminated, but Z is supported by fewer
than 50%+1.
S:  Again, IRVa ballots would be made as easy as possible for citizens to use by counting each candidate not marked as equally ranked ‘bottom’ except for the candidates who had been expressly ranked.  Consequently, in this example, IRVa would firstly give candidates A, B, C & X the option either publically to elect Z by giving at least two of their ‘default votes’ to Z, or instead, to give all four of their ‘default votes’ to A, B, C or X .  If either two of these four candidates refused to give their ‘default votes’ to Z, or A, B, C & X found themselves unable to give their four ‘default votes’ to A, B, C or X, sequentially one of the four would be eliminated by lot and required publically to give his ‘default vote’ to one of the other candidates.  This elimination and vote transferring process would continue until one of the candidates had received four votes.