# [EM] criteria compliance and strategic vulnerability

Chris Benham chrisbenham at bigpond.com
Sat May 21 22:26:27 PDT 2005

```Participants,
James G-A  and  I have have been discussing his "Voting
Methods:definitions and criteria" page off-list, but James now thinks it
would be a good idea if we took it on to the list,
starting with this my most recent message to him. The quotes are all of
James G-A  or myself.

James,

>The plurality criterion might be a good one to add. Should I cite
>Woodall for that? If so, which paper of his?
>
Probably this one:
http://groups.yahoo.com/group/election-methods-list/files/wood1994.pdf

In my message I deliberately referred to a  "version" of  the Plurality
criterion, because as I recently pointed out in an EM message addressed
to Russ,
Woodall likes to economise on axioms  and so doesn't include the
common-sense axiom that two ballots that differ only in that one doesn't
rank the one
candidate the other specifically ranks last should be
treated/interpreted as identical.

http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/014958.html

["Plurality:  if some candidate x has more first-preference votes than
some other candidate y has votes in total, then x's probability
of election must be greater than y's."

In his papers, Woodall likes to economise on axioms; so doesn't include
the common-sense axiom that a ballot that leaves one candidate
unranked should be treated/regarded  the same as a ballot that ranks
this candidate last and all the other candidates the same.
His  "votes in total" refers to explicit rankings in any position.

Incorporating this axiom, a "version" of the Plurality criterion  I like is

"If  some candidate x is ranked in first-place on more ballots than
candidate y is ranked above equal-last, then y can't win".]

For me,  Plurality and Minimal Defense are the real clinching arguments
that WV  is better than Margins (defeat-droppers).
But there are three plain rankings methods that I prefer to
Defeat-Dropper (WV); and they are  CDTT,IRV and  SCRIRVE and CNTT,IRV.

>Frankly, I'm not sure if I fully understand LNH and LNH. "Adding a
>preference to a ballot must not decrease the probability of election of
>any candidate ranked above the new preference." Does that mean adding a
>candidate who was previously not listed on the ballot?
>
If  by "listed"  you mean "ranked", then yes. Sometimes Woodall's
language seems to assume that the candidates' names are displayed somewhere,
and that voters vote on blank sheets of paper by writing down the names
of  candidates the voter wishes to "vote for" in order of preference
with the
highest-ranked at the  "top" of  the "list",  and the most-preferred
also written down "first" (in time). (That explains the "later" in LNHarm.)
I think at one point Kevin Venzke came up with a "pairwise" version that
is maybe a bit stronger:
"Adding a vote to A's pairwise tally versus B must not reduce the chance
of any candidate winning except B" (my paraphrasing)

> So my
>LPC is based on Blake's "secret preferences criterion". It seems that LPC
>is a good indicator of burying vulnerability, no?
>
In the sense that it is equivalent to complete invulnerability to
Burying, yes  But that is a very expensive property that is incompatible
even with Condorcet(Gross).

>IMO, two "consistency" criteria that are of greater practical importance
>>than the ones you list are "Mono-add-plump"
>>and "Mono-append".
>
>
>
>	Maybe, I don't know. Again, these criteria are not as widely accepted as
>monotonicity, participation, and consistency. They might have some merit,
>but I haven't personally discovered it yet.
>
>
I  don't know how anyone can think that "monotonicity"  (aka Woodall's
Mono-raise) is worth mentioning (and/or worrying about) and at the same
time wonder if
these two "have any merit".  I personally think that Mono-raise is nice,
but too expensive because its incompatible with Weak Burial Resistance.
Most of the criteria are "nice" and have at least some strong aesthetic
appeal, and the reason why we don't have a method that meets them all is
that some are
incompatible with others. They all have some "price". Some we insist on
at any price because they are about the fundamental aim of the method.
One of  these
for me is (Mutual ) Majority. Others are always on our shopping list
mainly because they are so "cheap", like Mono-add-plump and  Mono-append!.

>In any case they both should definitely have a higher number than does
>>plain IRV in the "paradoxical" row, and the
>>number for ER-IRV(whole) should be 4 or 5.
>
>
>
>	Why is that? You may have to refresh my memory since our discussion of
>ER-IRV(whole) was quite some time ago. I believe that I had a good
>conceptual reply to your last message on the topic, but I never got around
>to writing it.
>
>
There was a blunder in some of my posts on this topic regarding
ER-IRV(fractional). It is not easy to come up with a three candidate
scenario in which the Pushover-compressionists
can succeed with all their supporters carrying out the strategy, but the
strategy is still more tempting  than in plain IRV.
But there was nothing wrong with my example regarding ER-IRV(whole).

> 45:Right=Left>CentreRight
> 35:CentreRight>Right>Left
> 20:Left>CentreRight>Right
>
> First-preference tallies
> Right:45       CentreRight:35      Left:65
>
> CentreRight has the lowest tally, and so is eliminated then Right wins.
> This time no coordination was needed. As long as the Right suporters
> knew that Right had more first-prefernces than CentreRight, and a
> pairwise win against Left, then each individual Right supporter got an
> increased expectation by insincerely upranking Left from last to
> equal-first  with no risk.

This would also work if the numbers 45/35/20 were replaced with
be IRV1, ER-IRV(fractional)2,
ER-IRV(whole) 5!

>Probably WV should have a lower number  than Margins in the
>>"compromising-reversal"  row,  because sometimes
>>in WV  compromising-compression can be an effective "defensive strategy"
>>but to achieve the same effect those voters
>>in Margins  have to compromise-reverse.
>
>
>
>	That's interesting. Would you mind showing me an example? It sounds
>familiar, but I don't have anything like that on the surface (of my mind,
>or of my voting files).
>
>
This is classic  Ossipoff/Eppley/Tarr  stuff  from the Jurassic period
of  WV versus Margins. This is from Steve Eppley's site:

http://alumnus.caltech.edu/~seppley/Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm

_Example 2_:  The non-drastic defense voting strategy.

Suppose there are 3 alternatives /x/, /y/ and /z/.  Suppose the voters'
preferences regarding the alternatives are as follows:

_46%_ 	_10%_ 	_10%_ 	_34%_
/x/ 	/y/ 	/y/ 	/z/
/y/ 	/x/ 	/z/ 	/y/
/z/ 	/z/ 	/x/ 	/x/

That is, 46% of the voters sincerely prefer /x/ over /y/ and /y/ over
/z/, 10% prefer /y/
over /x/ and /x/ over /z/, etc.  Suppose the voters vote the following
rankings:

_46%_ 	_10%_ 	_10%_ 	_34%_
/x/ 	/y/ 	/y/ 	/z,y/
/z/ 	/x/ 	/z/ 	/x/
/y/ 	/z/ 	/x/

The votes of the 46% who voted /x/ over /z/ over /y/
misrepresent their preferences
since they prefer /y/ over /z/. (As above, this is the classic
"reversal" strategy.)
The 34% who ranked both /z/ and /y/ tied for best are part of a 54%
coalition
who voted /y/ over /x/ and no worse than tied for best.  Satisfaction of
/non-drastic
defense/ requires that /x/ must not be elected given these
34% who prefer /z/ over /y/ do not need to "drastically" rank /y/ over
/z/ to ensure
that /x/ is not elected, assuming satisfaction of /non-drastic defense/.

>at the weak burial resistance criterion, but I unfortunately found it
>somewhat confusing.
>
I'm sorry to hear that. Here it is:

> "If x is the CW (and wins), and on more than 1/3 of the ballots ranked
> above y and z; and afterwards on some of the ballots that rank y above
> x and x not below z, z's ranking relative to x is raised while keeping
> y ranked above them both, then if there is a new winner it cannot be y."

>As far as I understand CDTT-IRV, the basic strategic vulnerability is
>that if the sincere IRV winner X differs from the sincere Condorcet winner
>Y, X>Y voters will have an incentive to bury-reverse Y.
>
CNTT,IRV has that problem, but CDTT,IRV  is less vulnerable to Burial
than Defeat-Dropper(Winning Votes)  or any other plain rankings method
that meets
Mutual Majority, Smith(Gross) and Clone Independence.
Take this classic example:
49: A   (sincere is A>B)
24: B
27: C>B

The CNTT is the normal Smith set, that on these votes includes all the
candidates. CNTT,IRV elects A.
One of the definitions of the CDTT is "the set of candidates that all
have a majority strength beat-path to the candidates that have one to them."
The CDTT here is BC. In the IRV count, B is first eliminated  and so C
wins (an example of failing the Plurality criterion).
The  A supporters  can do nothing to get A into the CDTT, but they can
gain a result they prefer by voting sincerely.
The B supporters can do theselves no harm by voting B>A if  they want to.
Of course, unlike plain IRV, it fails Later-no-Help. The C supporters
help C by ranking B.

The horror  possible real-world scenario with this method is that  a lot
of voters are advised to truncate, producing the above election, by
those whose
agenda is to bring the method into disrepute so that they can get rid of
it.  But if the participants accept that the system is fair and
permanently in place,
and just try to get their preferred candidates elected, then it should
work well.
One possible political advantage  of  CDTT,IRV is that it can be sold as
an improved form of IRV.  I  think that is better than jumping in front
of the IRV
movement and shouting "Go Back! IRV is evil!".

Chris Benham

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