On 11/12/2016 7:53 AM, Jameson Quinn wrote:

2016-11-11 12:50 GMT-05:00 C.Benham cbenham@adam.com.au:

Yes. The guarantee you can give is "as long as the world is somewhere in
this restricted domain — that is, essentially, as long as there are no
Condorcet cycles and each voter naturally rejects at least one of the 3
frontrunners — this method meets FBC". This is much broader than any
guarantee you could give for a typical non-FBC method. For instance, with
IRV, the best you could say would be "as long as your favorite is
eliminated early or wins overall, you don't have to betray them", which
unlike PAR's guarantee is not something which could ever be generally true
about all real elections for all factions.

C: I have in mind voters who are inclined to Compromise, and so it's *
absolute guarantee* or it's nothing.  Smith//Approval also has a much
lower Compromise incentive
than does IRV  (which in turn has a much much lower Compromise incentive
then FPP).

You're suggesting that the sincere preferences are

35: C >> A=B
33: A>B >> C
32: B>A >> C

C:  I'm not "suggesting". I'm stating.

If you are 1 of the B>A>>C voters considering whether to strategically
vote B>>A=C, you have no strong motivation to do so, because your vote
alone is not enough to shift the winner to B. This is what I mean by "no
slippery slope".

C: One "vote alone" is very rarely enough to do anything, so I suppose
no-one has a "strong motivation" to vote.

I believe that in the election you gave, there is no way to tell what the
sincere preferences are.

C: From just the information on the ballots, of course not (like any
election).

Perhaps the B voters are strategically truncating A; perhaps the C voters
are strategically truncating B. So the "correct winner" could be either A
or B, but is almost certainly not C.

C: By "correct winner" I assume you mean the sincere CW. But there is
reason to assume there is one. And if the B voters are actively Burying C,
it could be C.

The "CD criterion" requires the system to elect C, merely to punish the B
voters; I think that's perverse, because, among other things, it means that
a system does badly with center squeeze, allowing the C faction to
strategize and win.

C: No, it merely says "not B".  But CD + Plurality say that it must be C.

Largely, it's because I think that Condorcet systems are strategically
counterintuitive, and hard to present results in. I think that will lead to
more strategy than a system like PAR. That's because PAR can make
guarantees that Condorcet systems can't.

C: Such as?  What exactly does "strategically counter-intuitive" mean?  An
example?

2016-11-12 10:45 GMT-05:00 C.Benham <cbenham@adam.com.au
mailto:cbenham@adam.com.au>:

 On 11/12/2016 7:53 AM, Jameson Quinn wrote:

 C: I have in mind voters who are inclined to Compromise, and so
 it's /absolute guarantee/ or it's nothing.   Smith//Approval also
 has a much lower Compromise incentive
 than does IRV  (which in turn has a much much lower Compromise
 incentive then FPP).

 C:  I'm not "suggesting". I'm stating.

 C: One "vote alone" is very rarely enough to do anything, so I
 suppose no-one has a "strong motivation" to vote.

In Smith//approval, one vote alone would shift the above honest
election; so the fact that it does not in PAR is indeed notable.

In particular: in PAR, there is no way for the B voters to strategize
such that they win the above election, while still ensuring that C
does not win no matter what the A voters do. This "safe" strategizing
is grease on the slippery slope.

 C: From just the information on the ballots, of course not (like
 any election).

 C: By "correct winner" I assume you mean the sincere CW. But there
 is reason to assume there is one. And if the B voters are actively
 Burying C, it could be C.

 C: No, it merely says "not B".  But CD + Plurality say that it
 must be C.

 C: Such as?  What exactly does "strategically counter-intuitive"
 mean?  An example?

What I mean is that if you take a non-election-theorist, present an
election scenario to them, explain who won and why, and ask how they
would strategize in the place of voter X, they are more likely to
suggest counterproductive strategies, and less likely to see any
strategies that actually might work, in Condorcet than in Bucklin-like
systems.

 C:  Your method and MJ fail IIA.

MJ passes IIA. PAR fails it, as you say, but passes LIIA.

Prefer Accept Reject (PAR) voting works as follows:

1. Voters can Prefer, Accept, or Reject each candidate. Blanks
   count as "Reject" if no rival is explicitly rejected; otherwise,
   blank is "Accept".
2. Candidates with at least 25% Prefer, and no more than 50% reject,
   are "viable". The most-preferred viable candidate (if any) is the
   leader.
3. Each "prefer" is worth 1 point. For viable candidates, each
   "accept" on a ballot which doesn't prefer the leader is also worth
   1 point. Most points wins.

I would be a bit surprised if IIA can be met by a method (such as MJ and
Bucklin) by a method that fails Irrelevant Ballots Independence.

There is some rubbish about Independence of Irrelevant Alternatives (IIA)
on Electowiki.  I'll address that in a later post.

Chris Benham

On 11/13/2016 3:35 AM, Jameson Quinn wrote:

2016-11-12 10:45 GMT-05:00 C.Benham cbenham@adam.com.au:

In Smith//approval, one vote alone would shift the above honest election;
so the fact that it does not in PAR is indeed notable.

In particular: in PAR, there is no way for the B voters to strategize such
that they win the above election, while still ensuring that C does not win
no matter what the A voters do. This "safe" strategizing is grease on the
slippery slope.

What I mean is that if you take a non-election-theorist, present an
election scenario to them, explain who won and why, and ask how they would
strategize in the place of voter X, they are more likely to suggest
counterproductive strategies, and less likely to see any strategies that
actually might work, in Condorcet than in Bucklin-like systems.

MJ passes IIA. PAR fails it, as you say, but passes LIIA.

Prefer Accept Reject (PAR) voting works as follows:

1. *Voters can Prefer, Accept, or Reject each candidate.* Blanks count
as "Reject" if no rival is explicitly rejected; otherwise, blank is
"Accept".
2. *Candidates with at least 25% Prefer, and no more than 50% reject,
are "viable"*. The most-preferred viable candidate (if any) is the
leader.
3. Each "prefer" is worth 1 point. For viable candidates, each
"accept" on a ballot which doesn't prefer the leader is also worth 1 point. *Most
points wins.*

2016-11-13 6:34 GMT-05:00 C.Benham <cbenham@adam.com.au
mailto:cbenham@adam.com.au>:

 On 11/13/2016 3:35 AM, Jameson Quinn wrote:

 The strategy incentives for Condorcet voting methods vary widely. 
 Some have a random-fill incentive while others have a truncation
 incentive. Some have
 a stronger or weaker incentive to equal-top rank than others, and
 some are more vulnerable to Burial than others.

 Smith//Approval has a truncation incentive like Bucklin's, only
 less strong. In addition Bucklin has an equal-top rank/rate
 incentive.  I don't see the problem.

 BTW, why does it matter if "non-election-theorists" when asked
 suggest "counter-productive strategies"? Shouldn't we be
 encouraging sincere voting?
 If they don't want to do that, why can't they just take the
 strategy advice of their favourites?

My concern here is that people will misuse strategy. I think that FBC
and IIA are good guarantees to be able to give, but also that these
guarantees are related to O(N) summability, which is basically saying
"you can think about what's going on in an election, it fits inside
your head." PAR does not have O(N) summability, but it can be done in
2 steps, each of them O(N) summable, and each of them considered
separately meeting FBC and IIA.

 35: C >> A=B
 33: A>B >> C
 32: B>A >> C

 I don't see why.  The example I gave just happened to have a close
 CW.  PAR seems to give an A=B tie unless (as I assume) it breaks
 tied final
 scores in favour of the "leader" (A).

 Of course, that is why it's called a "chicken dilemma".  In what
 method /can/ "the B voters to strategize such that they win the
 above election, while still ensuring that C does not win no matter
 what the A voters do" ??

I think that you still don't understand what I mean by "slippery
slope". (Of course, once you do understand it, you're still free to
disagree that it's important.)

Suppose you have a scenario like the following:
19: A>B
11: ??? A or A>B ??? (more generally: either a bullet vote for A, or a
vote with A top, B second-to-bottom, and all else bottom. In approval,
then, this would be A or AB)
25: (ego faction; true preferences B>A)
45: C

You are in the ego faction, and deciding whether to vote B>A or just B
(or in approval, BA or B). If there is some combination of votes that
the ego faction can give such that B wins in the case where the 11
votes are B>A, but A wins in the case where the 11 votes are A, then
there is a slippery slope; the ego faction can safely and profitably
use a small amount of offensive strategy, which means that A voters
should use slightly more defensive strategy, and then there's a cycle
of escalation until both factions fall off the cliff and end up
electing C.

Is that clear now?

 As do some Condorcet methods. It isn't one of the criteria I care
 much about.

 As I understand it, IIA can only be met by methods that fail
 Majority (like positional methods that pretend that the voters'
 ratings are on some scale independent of the
 candidates).   MJ  is a variety of Median Ratings which is
 normally claimed to meet Majority.

IIA, when applied to a cardinal or categorical method, assumes that
when you remove a candidate, you simply delete that candidate from all
ballots and leave them otherwise unchanged.

The definition of majority used in the proof that IIA and Majority are
incompatible assumes otherwise. Thus, this proof does not apply to
non-ranked methods. Or perhaps one could say: it shows that a method
cannot pass IIA and ranked-majority. MJ does not pass ranked-majority,
but it does pass majority, so that's fine.

MJ does pass IIA.

 I would be a bit surprised if IIA can be met by a method (such as
 MJ and Bucklin) by a method that fails Irrelevant Ballots
 Independence.

 There is some rubbish about Independence of Irrelevant
 Alternatives (IIA) on Electowiki.  I'll address that in a later post.

 Chris Benham



 On 11/13/2016 3:35 AM, Jameson Quinn wrote:

2016-11-13 6:34 GMT-05:00 C.Benham <cbenham@adam.com.au
mailto:cbenham@adam.com.au>:

 On 11/13/2016 3:35 AM, Jameson Quinn wrote:

 The strategy incentives for Condorcet voting methods vary widely. 
 Some have a random-fill incentive while others have a truncation
 incentive. Some have
 a stronger or weaker incentive to equal-top rank than others, and
 some are more vulnerable to Burial than others.

 Smith//Approval has a truncation incentive like Bucklin's, only
 less strong. In addition Bucklin has an equal-top rank/rate
 incentive.  I don't see the problem.

 BTW, why does it matter if "non-election-theorists" when asked
 suggest "counter-productive strategies"? Shouldn't we be
 encouraging sincere voting?
 If they don't want to do that, why can't they just take the
 strategy advice of their favourites?

My concern here is that people will misuse strategy. I think that FBC
and IIA are good guarantees to be able to give, but also that these
guarantees are related to O(N) summability, which is basically saying
"you can think about what's going on in an election, it fits inside
your head." PAR does not have O(N) summability, but it can be done in
2 steps, each of them O(N) summable, and each of them considered
separately meeting FBC and IIA.

 35: C >> A=B
 33: A>B >> C
 32: B>A >> C

 I don't see why.  The example I gave just happened to have a close
 CW.  PAR seems to give an A=B tie unless (as I assume) it breaks
 tied final
 scores in favour of the "leader" (A).

 Of course, that is why it's called a "chicken dilemma".  In what
 method /can/ "the B voters to strategize such that they win the
 above election, while still ensuring that C does not win no matter
 what the A voters do" ??

I think that you still don't understand what I mean by "slippery
slope". (Of course, once you do understand it, you're still free to
disagree that it's important.)

Suppose you have a scenario like the following:
19: A>B
11: ??? A or A>B ??? (more generally: either a bullet vote for A, or a
vote with A top, B second-to-bottom, and all else bottom. In approval,
then, this would be A or AB)
25: (ego faction; true preferences B>A)
45: C

You are in the ego faction, and deciding whether to vote B>A or just B
(or in approval, BA or B). If there is some combination of votes that
the ego faction can give such that B wins in the case where the 11
votes are B>A, but A wins in the case where the 11 votes are A, then
there is a slippery slope; the ego faction can safely and profitably
use a small amount of offensive strategy, which means that A voters
should use slightly more defensive strategy, and then there's a cycle
of escalation until both factions fall off the cliff and end up
electing C.

Is that clear now?

 As do some Condorcet methods. It isn't one of the criteria I care
 much about.

 As I understand it, IIA can only be met by methods that fail
 Majority (like positional methods that pretend that the voters'
 ratings are on some scale independent of the
 candidates).   MJ  is a variety of Median Ratings which is
 normally claimed to meet Majority.

IIA, when applied to a cardinal or categorical method, assumes that
when you remove a candidate, you simply delete that candidate from all
ballots and leave them otherwise unchanged.

The definition of majority used in the proof that IIA and Majority are
incompatible assumes otherwise. Thus, this proof does not apply to
non-ranked methods. Or perhaps one could say: it shows that a method
cannot pass IIA and ranked-majority. MJ does not pass ranked-majority,
but it does pass majority, so that's fine.

MJ does pass IIA.

 I would be a bit surprised if IIA can be met by a method (such as
 MJ and Bucklin) by a method that fails Irrelevant Ballots
 Independence.

 There is some rubbish about Independence of Irrelevant
 Alternatives (IIA) on Electowiki.  I'll address that in a later post.

 Chris Benham



 On 11/13/2016 3:35 AM, Jameson Quinn wrote: