[EM] Kristofer and Steve on IRVa vs. MAM

Wed Jun 1 14:14:57 PDT 2016

On 05/30/2016 04:53 PM, steve bosworth wrote:
> 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.’

What is the definition of "average intensity of preference"?

I tend to think that it's generally impossible to directly infer
enthusiasm from a ranked ballot, since we're dealing with ordinal data.
All you can say is whether "X likes Y more than X likes Z". You can't
know whether a ballot like

A>B>C>D>E>F

is

"I really like A, B, and C; I think D and E are so-so, and I loathe F"

or if it is

"I really like A, I think B is so-so, and I hate everybody else, but I'd
rather have C than D, D than E, E than F".

In other words, the rankings themselves can't tell you whether

A>B>C>D

is

Washington > Lincoln > Bush > Khrushchev

or if it is

Lincoln > Khrushchev > Lenin > Stalin,

and how much weight you should put on first place compared with second
place is obviously different for these two scenarios, as far as
intensity is concerned.

The general approacah for dealing with intensity of ranking is to use
ratings instead, or use something like Majority Judgement where you're
permitted to skip ranks and each rank has a name ("Excellent", "Good", etc).

As for the MAM example, it seems that F wins in MAM as well.

If I'm not mistaken, your vote set is

38: F
23: G>F
25: E
9: M>N>E
5: K>P>E

candidates: E F G K M N P

The Condorcet matrix (row beats column) is

Option	E	F	G	K	M	N	P
E	0	39	39	34	30	30	34
F	61	0	38	61	61	61	61
G	23	23	0	23	23	23	23
K	5	5	5	0	5	5	5
M	9	9	9	9	0	9	9
N	9	9	9	9	0	0	9
P	5	5	5	0	5	5	0

The wv matrix is

Option	E	F	G	K	M	N	P
E	0	0	39	34	30	30	34
F	61	0	38	61	61	61	61
G	0	0	0	23	23	23	23
K	0	0	0	0	0	0	5
M	0	0	0	9	0	9	9
N	0	0	0	9	0	0	9
P	0	0	0	0	0	0	0

So the first few lock-ins go (equal strength defeats broken in
alphabetical order for simplicity):

1. F>E with 61 votes
2. F>K with 61 votes
3. F>M with 61 votes
4. F>P with 61 votes

Clearly, E can't possibly beat F since F is locked ahead of E on the
very first step. You must have calculated the Condorcet or wv matrix
incorrectly. In fact, regardless of whether you use wv or margins, F
becomes the CW: he beats everybody else pairwise.

If you'd like to check the calculation for other ballot sets,
http://www.ericgorr.net/condorcet/ will give both the Condorcet matrix
and the wv matrix when verbosity is set to "Tell me some things" or
"Tell me everything".

It'll also show what pairs MAM locks if you set it to "Tell me
everything", although it may not show them in order of defeat strength;
it locks large numbers of pairs at once when it knows that it can do so
without causing a cycle.

I'll further comment on a few others, as much as I have time to at least:

> 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,

- As do all -a methods.

> 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

I'm not sure what that means.

> 3)      that the winner will be supported more enthusiastically than any other candidate.’

Consider this example from rangevoting.org:

10: 	G > C > P > M
3: 	C > G > P > M
5: 	C > P > M > G
6: 	M > P > C > G
4: 	P > M > C > G

IRV elects M. But M only has 6 first preferences whereas C, the
Condorcet winner, has 8. Since C is the Condorcet winner, it's also
supported by a majority, so majority support can't be the reason C
doesn't win in IRV.
So if first preferences is the metric of enthusiasm, IRV fails.

And if it isn't, then it's possible to construct examples where:

	- some candidate A has one more first preference vote than some other
candidate W,
	- A has no second place preferences,
	- W has some constant c number of second place preferences,
	- A wins in IRV,
	- W is the Condorcet winner,

meaning that if one first place vote is worth x second place votes, then
you can make IRV choose wrong no matter what x is.

E.g. for x=14:

4:      W>B>A>C>D
5:      A>W>B>C>D
5:      C>W>A>B>D
5:      D>W>A>B>C

W has 4 first preferences and A has 5. W has 15 second preferences (A
has none) and A has 14 third preferences.

So either enthusiasm is only based on first preferences, in which case
the first example shows that IRV gets it wrong, or it's based on first
*and* second preferences, in which case the second example would make
IRV get it wrong.

There's a continuum argument hiding in here, though I don't have time to
go into it in detail. Briefly: IRV is more Plurality-like than Condorcet
and more Condorcetian than Plurality. So any argument that favors IRV
has to show that the argument can't be taken to its logical conclusion
to favor either Condorcet or Plurality just as strongly.

> 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.

Suppose we conduct a presidential election by Approval ("thumbs up" or
"like") voting, and there are 5 candidates. That is, each voter gets a
list of the 5 presidential candidates and is told to place a mark by
each candidate he likes. The candidate with the most likes/approvals wins.

Now suppose that voter A chooses to approve of two candidates, while
voter B chooses to approve of three. Does that violate one citizen one
vote? After all, voter A "spent" two points (gave points to two
candidates) while B "spent" three.

I'd say no, because each ballot has one state for each candidate: either
liked or unliked. Each ballot adds the same information to the voting
pool: whether the candidate chose to strengthen candidate X, candidate
Y, candidate Z, etc... So if there are 5 candidates, each ballot has 5
aye/nay votes, and each voter spends 5 such votes. The voter who liked
two candidates used 2 ayes and 3 nays, and the other voter used 3 ayes
and 2 nays.

Analogously, a Condorcet election could be conducted by asking the voter
"in which of these runoffs would you support the first candidate on the
ballot?". There are n^2 hypothetical runoffs for n candidates, so that
kind of ballot would have n^2 aye/nay votes.

In a three candidate election, someone who votes

A>B>C

would say aye to "would you support the first candidate on the ballot in
an A vs B runoff?", "in an A vs C runoff?" and "in a B vs C runoff?",
and nay to all the others. It's just that, to spare the voter from
having to fill out a bunch of tedious yes/no questions, the method
infers the answer to these aye/nay questions from a ranked ballot.

And if the Approval ballot doesn't violate one man one vote, then
neither does the Condorcet ballot. Yes, some voters increment more
runoffs than others (if there's equal rank and truncation), but deciding
to *not* increment someone's runoff is also a vote.

>>he helps C more by protecting C from A and B, i.e. by increasing A>C and
>> A>B.
> 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.

Either I meant that he helps C by protecting C from an increase of A>C
and from an increase of A>B, or that was a typo. In either case, what I
meant was that if someone raises C, the number of votes it takes to make
A beat C is also increased.

I could probably have made that clearer.

> 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.

Monotonicity failures require multiple ballot sets. See
http://www.rangevoting.org/Monotone.html. My point is that the voter's
power is an unpredictable function of his ranking. If he moves a
candidate higher on his ranking, he may cause the candidate to lose and
vice versa. That's not something that says "equal power" to me.

Under no method (except possibly Random Pair, Random Dictator, and
combinations of them) are votes completely equal in power anyway. It
depends on what they vote and when they do it. Suppose you have a
majority election:

51: A
50: B

and two voters show up, and they're the last two voters of the election.
If they vote for B, they change the outcome (great power); if they vote
for A, nothing happens (not so much).

>> K: * That is, unless there are truncated ballots, but then IRV doesn't give
>> a majority either.
> This is why I added ‘Asset Voting’ to IRV, to produce IRVa.

Yes, but we were initially talking about IRV without -a:

>>> However, before I do that, I want to claim that in comparison to all
>>> other electoral system not using the above asset voting, APR (also
>>> without this asset addition) still does all it could do to allow each
>>> citizen to guarantee that her one vote will be added to the weighted
>>> vote of the one elected candidate of all the pre-established number of
>>> the assembly’s members whom she most trusts to speak, work, and vote
>>> faithfully on her behalf. Do you agree? Also in this case, this
>>> simplified APR might waste some votes.

That's what I was responding to.