[EM] The two extremes of voting-system strategy-advantage

[Michael Ossipoff]

Of course there are all sorts of standards and criteria by which voting
systems can be compared and regarded. But I'm not the only person whose
interest in voting systems is about strategy.
I suggest that there are two classes of methods that represent two extremes
of voting system strategy advantages. ...and that that voting-systems
distinction and division is significant.
I refer to these two classes of voting systems:
1) Approval and a few strategically-similar methods (Score, ICT, and
Symmetrical ICT, and maybe others).
.
2) IRV and its Condorcet hybrids
Those two classes of methods represent two extremes of voting system
strategy advantages.
The 1st class, I've named "Approval etc.", or Approval&c, further
abbreviated to A&c.
The 2nd class, I'll call "IRV etc.", or IRV&c, further abbreviated to I&c.
(I'm using the name "IRV" instead of AV or Preferential Voting, because IRV
is now best known by that name, and is offered
by that name in the platforms of at least 5 U.S. political parties.)
Approval&c:
---------------
Other than its compliance with all of the monotonicity and consistency
criteria, Approval's main criterion advantages are its compliance with the
Favorite-Betrayal Criterion (FBC) and Later-No-Help (LNHe).
Symmetrical ICT meets FBC, and an insignificantly weaker version of LNHe,
which I call 0-info LNHe. I've defined it here, and at electowiki.
But maybe I should repeat it here:
0-info LNHe (ZLNHe):
In a 0-info election, voting for one or more candidates in set S shouldn't
decrease the probability that the winner will be from S.
To vote for a candidate is to vote that candidate over at least one other
candidate.
(In earlier postings, I've given two general, universally-applicable,
definitions of voting X over Y)
[end of ZLNHe definition]
Like LNHe, ZLNHe relieves voters of the need to vote for unacceptable
candidates, greatly easing the task of voting when there are many
candidates.
Symmetrical ICT additionally brings compliance with CD. Symmetrical ICT
automatically avoids the chicken dilemma. I suggest that Symmetrical ICT
(SITC) could be regarded as Approval with CD.
Approval, Score, ICT and Symmetrical ICT, I refer collectively to as
Approval etc., Approval&c, or A&c.
Symmetrical ICT meets the Condorcet Critrerion when CC is defined in a
general way (arguably the more legitimate way).
But all A&c tend to elect CWs.
Though Approval and Score don't meet CD, they have a good way (strategic
fractional ratings) of dealing with chicken dilemma. For that and other
reasons (described in previous postings here) the chicken dilemma won't be
a problem with Approval and Score (or, of course with CD-complyng ICT and
Symmetrical ICT).
Approval and Score, and, to a large extent, all A&c, have great stability.
I've often referred to Approval as a solid and reliable handtool, as
opposed to idiosyncratic labor-saving contraptions.
A&c are the methods of choice where FBC is needed, as it is under current
conditions.
Approval's opponents want to fully vote X over Y, and Y over Z. They'd like
to be allowed that, but the catch is that most methods that allow that give
strategic incentive or need to do so insincerely, which really defeats the
whole purpose of it.
Approval lets you reliably and fully vote a preferred set over an
unpreferred set. The importance and power of that shouldn't be
underestimated. You can easily, simply, fully vote all the acceptable
candidates over all the unacceptable candidates, and that will be reliably
and simply counted. And that's what matters in a u/a election. With various
kinds of experimental test-voting, and with probabilistic strategic
fractional rating, it's possible to begin choosing among one's preferred
set too.
Strategy in Approval:
 If it's a u/a election, then it's especially simple; Just approve the
candidates who are acceptable.
Say it's non-u/a:
Some people express a need to vote in a way that is optimal, in terms of
the actual (unknowable) configuration of other people's votes. But is that
necessary? Maybe it's enough to vote in a way that's optimal in terms of
your perception of the situation. You can do that by approving the
candidates you like, the ones you trust. If it's a u/a election, then it's
especially simple; Just approve the candidates who are acceptable. But here
I'm talking about non-u/a.
If you want to make it unnecessarily more difficult, you could, before
approving a candidate, ask yourself such questions as "Does s/he feel more
like a protection, or a menace, if I approve hir?", or " Are the better
candidates really so good that you don't want that compromise? Are the
worse candidates really so bad that you want that compromise?" "Which feels
greater, the threat of someone worse winning, or the promise of someone
better winning?". Or "How far does it feel like i need to compromise--who's
likely the best I can get?" ...etc.
Then, too, you're voting in a way that's optimal in terms of your feelings,
your perception of the situation. That might not sound as good as voting in
a way that's optimal in terms of the actual unknowable configuration of
other people's votes, but why not? After all, the other voters don't know
more than you do, so you're not at a disadvantage. And if everyone approves
those whom they like, then we get the candidate liked by most.
Optimality in terms of your likes, feelings or perceptions, as opposed to
the actual unknowable configuration of other people's votes, is a
completely different way of regarding the election, and how to vote. But
it's just as valid, and works just as well, for the individual voters and
for society.
In summary, Approval is a lot better than people think it is.
But many want the "rank-balloting ideal"--They want to fully protect their
preferred set (as they so easily can in Approval), while still having an
easy, strategy-free choice _among_ their preferred set. They want entirely
strategy-free voting. I don't think that's necessary. Approval, or other
A&c, would be fine, under any conditions.
But the rank-balloting ideal is achievable, for some voters--the ones in a
mutual majority (MM). (Of course Gibbard & Satterthwaite pointed out that
it can't be reliably available to everyone).
IRV&c:
----------
The popularity of the rank-balloting ideal can be judged by the great
popularity of IRV. As mentioned above, at least 5 U.S. political parties
offer IRV in their platforms. IRV is the only alternative voting system
offered in a party platform.
As noted above, the rank-balloting ideal is achievable, at least for
MM-members--and that's good enough.
That's the other, opposite, strategy-advantage extreme for voting systems.
Of course every advantage comes at a price--some disadvantage, or the loss
of some other advantage
In the case of IRV, its strategy-freeness for MM-voters comes at the cost
of favorite-burial need for non-MM voters, mostly caused by lower Condorcet
efficiency, and the prohibition against equal ranking. That isn't
undemocratic or unfair, because there's nothing wrong with government by a
cohesive majority.That's ok.
The failure to elect a CW can, itself, count as a disadvantage, when it
displeases CW-preferrers, causing them to side with the non-MM voters in a
vote to replace IRV with something more Condorcet efficient. The
disadvantages named in this and the previous paragraph could result in a
majority voting to replace IRV with a more Condorcet efficient method.
That's ok too.
It isn't that IRV isn't a good method (for the Green scenario). It's just
that it could be vulnerable to replacement with something that better
elects CWs.
But, other than that, not electing the CW isn't as bad as some seem to
think it is. If the MM vote sincerely, then IRV chooses from the MM
preferred set. How important is it which member of that set is chosen? To
give an example, I just want to elect a progressive. I don't care which
one. I'd be glad to approve them all in Approval. Well, if I'd help them
all in Approval, because I just want one f them to win, then why should I
start caring a lot which one wins when the method is IRV? It's enough that
IRV would choose from the MM preferred set.
...But, as I said, that might not be ok with the CW preferrers, when the CW
isn't chosen. Because that would displease them, and the non-MM voters,
then IRV might get replaced. Those 5 political parties want IRV in spite of
that, and there's nothing wrong with their finding out from experience that
they'd prefer something more Condorcet-efficient. That's ok.
Some people get all hysterical about failure to choose the CW, but if it
bothers a majority, they'll change the method. Don't worry. It's going to
be alright.

When IRV doesn't choose the CW, it's often because someone else in the
MM-preferred set is more popular than the CW. What's wrong with that?
For Green scenario conditions, IRV is a lot better than some people think
it is.
Nevertheless, that CW-elimination disadvantage, with the resulting
replacement-vulnerability for IRV can be avoided.
I've spoken of the Condorcet-IRV hybrids, of which James Green-Armytage
described four, in his article at http://econ.ucsb.edu/~armytage/hybrids.pdf
A simpler one is Unbeaten//IRV:
If there's a candidate with no pairwise defeats, then elect hir. If there
isn't one, then do IRV among all of the candidates.
(Of course, if there are more than one unbeaten candidate, then you could
do IRV just among those)
It might be tempting to say to do IRV among the Smith set. That's
Smith//IRV, one of James' hybrids. But James points out that Smith//IRV
fails Mono-Add-Plump and Mono-Append.
All four of James' hybrids meet the Smith Criterion.
Another way of avoiding or mitigating IRV's disadvantage would be what
could be called Approval IRV, or AIRV:
Equal ranking allowed. If you rank several 1st choices, they all get an
initial whole vote from you.
When all of your candidates at rank N are eliminated, then all of your
candidates at rank N + 1 each get a whole vote from you.
In my brief IRV definition, that amounts to saying that a candidate tops a
ranking if s/he is one of the candidates at that ranking's highest rank
position that has uneliminated candidates.
Though AIRV isn't as good as the Condorcet-IRV hybrids, I'll include AIRV
in IRV&c (I&c), as one of the ways to avoid IRV's disadvantages.
Another hybrid:
Dennis Hill said to, at each stage of IRV, exempt the current CW from
elimination.
Benham said to elect that CW when one appears.
I don't know which hybrid, of those mentioned by James, and any others, is
better, but, collectively, they're my favorite methods for the Green
scenario.
That's mostly because 1) Rank balloting and the rank-balloting ideal are of
great interest to progressives; and 2) Experience with polling suggests
that people do better with Score than with Approval, and that they do
better with rankings than with Score; 3) Of course we'd all like the luxury
of the rank-balloting ideal.
Personally, as an individual voter, I'd have no objection, even in the
Green scenario, to Approval, Score, ICT or Symmetrical ICT, because
choosing among the progressive candidates wouldn't be so important to me.
------------------------------------------------------
Anyway my point in this post is that A&c and I&c are the opposite extremes
of an important strategy-advantage distinction. ...and that that
distinction is significant for classifying voting systems, because of the
universal agreement about the desirability of the rank-balloting ideal.
Though I refer to them as extremes, I'm not saying that there are methods
between them. Those "extremes" consist of the strategically desirable
voting systems.
Of course there are methods that don't qualify for either classification,
and I don't say that those are "between" A&c and I&c.
-------------------------------------------------------
IRV brings MM voters strategy-freeness at a cost, as described above. The
cost is worth it, but it can be avoided, as described above, by the hybrids
or AIRV.
IRV doesn't really have a strategy-requirement, for MM  voters to be able
to make IRV work. Sure, a mutual majority would have to be voted as
such--but why wouldn't it be?
The methods that avoid IRV's cost the (hybrids) likewise bring their own
cost. Some degree of ethics or consideration of consequences is needed. As
is so often the case, with power comes a requirement for responsibility, if
you are to benefit from it. I think that the voters will qualify for
successful use of the hybrids.
AIRV mitigates IRV;s disadvantage by allowing Approval-like voting.
Under Green scenario conditions, there's a case for IRV, the hybrids, or
AIRV.
In fact, of course, even under Green scenario conditions, there's a case
for A&c too.
Michael Ossipoff
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