# [EM] Approval Voting and Long-term effects of voting systems

Sun Dec 11 21:52:19 PST 2016

```On 12/9/2016 10:05 AM, Michael Ossipoff wrote:

> The fact of it being better to equal-rank the set that is important to
> you instead of choosing among them is true with other rank methods too.
>
> In particular, it's true of Condorcet & Bucklin. It would be true of
> IRV too, if IRV allowed equal-ranking.
>
> I don't have proof that it's, in principle, a property of _all_
> ranking-methods, but I don't know of an exception.

Mike,

If  IRV allows equal-ranking, it should definitely be the "fractional"
version (so that in every round each ballot gives a single vote or
fractions of a vote
that sum to 1).

If instead a ballot gives a full vote (approval style) to each candidate
it highest ranks then the method is much more vulnerable to Pushover and
fails
Mutual Dominant Third.   I gave an example of that a while (probably
years) ago.

Here is an example of Push-over that is also a failure of Unburiable
Mutual Dominant Third:

45: A=C  (sincere is A>B)
35: B>A
20: C>B

B is the sincere MDT candidate, and so with normal IRV is strategically
invulnerable, but under  ER-IRV(Whole) loses to A.

The fractional version also makes Push-over strategising a bit easier,
so for IRV and Benham I'm opposed to allowing above-bottom
equal-ranking.

But if that is insisted on I suggest that to decide which candidate is
next eliminated we first order the candidates by the fractional method,
and then have ballots that equal-highest rank more than one candidate
give a full vote to the one of those that is highest in the order (and
nothing to any other candidate).  Then eliminate the candidate with the

So in the above example the initial order is  C 40.5  >  B 35 >  A
22.5.   The 45 A=C ballots give a full vote to C, giving C 65 > B 35 > A
0.  We eliminate
A and then B and C wins.   (There are better examples where the device
does some good).

You wrote "I don't have proof that it's, in principle, a property of
_all_ ranking-methods, but I don't know of an exception."

It's true of  Winning Votes and Bucklin and any of the proposed methods
that meet FBC, but I don't see how it is of ER-IRV(fractional).

Or MinMax Margins or  ER-Benham(fractional)  or even Smith//Approval
(implicit).

In the latter case obviously the voter should truncate hir bottom-set,
but couldn't it be the case that if the voter strictly ranks hir top set
then one
of them will be the CW while the most approved candidate is in hir
bottom set but if the voter equal top-ranks hir top set there will be a
top-cycle
that includes the most approved candidate?

Chris Benham

On 12/9/2016 10:05 AM, Michael Ossipoff wrote:
>
>
> When I used the example of MDDA & MDDAsc, to illustrate that it's
> better to equal-top-rank your strong top-set, rather than choosing
> among them by ranking them in order of preference--That wasn't
> intended as criticism of MDDA & MDDAsc.
>
> The fact of it being better to equal-rank the set that is important to
> you instead of choosing among them is true with other rank methods too.
>
> In particular, it's true of Condorcet & Bucklin. It would be true of
> IRV too, if IRV allowed equal-ranking.
>
> I don't have proof that it's, in principle, a property of _all_
> ranking-methods, but I don't know of an exception.
>
> One fairly obvious thing that can be said for MDDA & MDDAsc is that
> your protection for your strong top-set, even when ranking them (and
> no one else) in order of preference, and approving them all (as is the
> default), is as good as your protection of them in Approval, when you
> approve only lthem.
>
> A majority doing so in approval will elect one of them.
>
> A majority doing so in MDDA or MDDAsc will give a
> majority-disqualification to everyone else. And if preferrers of one
> of your strong bottom-set try burial or truncation, and if they
> thereby manage to make everyone majority-disqualified, then someone in
> your strong set will win the Approval count.
>
> That suggests that MDDA & MDDAsc let you choose among your strong
> top-set, and still protect them from your strong bottom-set just as
> well as Approval would have let you. That's an improvement over Approval.
>
> Of course an additional improvement is that MDDA & MDDAsc give you an
> easy, convenient, & reliable way to avoid chicken-dilemma (by denying
> approval to the candidate of the distrusted faction.
>
> It's just that MDDA & MDDAsc allow you to further enhance the
> protection of your strong top-set, by top-ranking them all. If a
> majority do that,then it would be quite impossible for buriers or
> truncators to majority-disqualify them. Of course if any significant
> number of voters similar to you top-rank those candidates, that makes
> it much more difficult, or impossible, for buriers or triuncators to
> majority-disqualify them.
>
> If you use the chicken-dilemma defense of denying approval to the
> candidate of the distrusted faction, and that candidate is someone
> whom you top-rank, then you're still protecting hir from burial &
> truncation, for the reason described above.
>
> If the candidate to whom you deny approval is someone you rank below
> top, then that is no longer true. If the method is MDDA, that
> candidate still has the full truncation-proofness protection that any
> ranked candidate has. If the method is MDDAsc, that is no longer
> guaranteed. But, if Mono-Add-Plump is necessary for public acceptance,
> then the cutting-loose of that middle-ranked candidate of the
> distrusted faction is a regrettable but justifiable action resulting
> from reasons that that faction has given you for defection-deterrence.
>
> Likewise, though MDDA protects your middle-ranked candidates from
> truncation by eachother's factions, that protection isn't essential,
> because reliably choosing _among_ your strong top-set isn't the
> important thing.
>
> In MDDAsc, you're still fully protecting your top-ranked candidates
> against everyone else, and you're still fully protecting all of your
> rannked & approved candidates against your unranked, unapproved
> candidates. That's what's important.
>
> MDDA & MDDAsc are the rank methods that best deliver the benefits that
> are available from ranking-methods.
>
> Now, to resum my reply:
>
>
>     I like to remind people that, very often, "Good enough is better
>     than best."  That is, a voting system (or a candidate) that is
>     "good enough" may very likely better than one that is "best".
>
>
> Exactly. Eecting one that is good enough is much more important than
> reducing the probability of doing so, by trying to choose among the
> ones that are good enough.
>
>
>
>
>
>         1. In this country, for the 99%, a progressive government
>         would be incomparably better than a Republocrat government
>         (like we've had for a long time, and still have).
>
>         If you don't believe it, look at some progressive party
>         platforms (Greens, etc.), and compare them to the things that
>         people are saying that they want, or that they want changed.
>
>         So, for the 99%, _any_ progressive would support better
>         policies than_any_ republocrat.
>
>         That means that, for the 99%, there's a strong top-set and a
>         strong bottom-set.
>
>         ...And, when there is, Approval voting is really simple:
>
>         Approve (only) all of your strong top-set.
>
>         2. Suppose we're talking about a better world, in a better
>         future, in which the 99% don't have a bottom-set. Or suppose
>         we're talking about some other country, or some entirely
>         different non-political voting-situation.in
>         <http://voting-situation.in> which you don't have strong top &
>         bottom sets.
>
>         There are various ways that you could vote.
>
>         a) If you wanted to, and if any reliable predictive
>         information is available, then you could use it for tactical
>         voting. (We're talking about voting in Approval).
>
>         b) If not, you could, if you wanted to, try to estimate where,
>         in the candidate lineuup, your merit-expectation is, and
>         approve down to there, as an expectation-maximizing strategy.
>         Depending on what is known or felt about the relation between
>         the distributions of voters & candidates, you could approve
>         down to the mean, the mid-range, or the median, of the
>         candidates' merits.
>
>         Of course the median & midrange would be easiest: The midrange
>         is the point halfway between the worst & the best. But easiest
>         of all is the median. You'd approve the best half of the
>         candidates. That could be regarded as a rough estimate for the
>         other two central-tendency measures, when they're difficult to
>         estimate.
>
>
>     "Approve about half" is a good enough, easy to remember
>     guideline.  It would seem to maximize your impact as well.
>
>
> Yes, you're voting between the maximum number of candidate-pairs.
>
>
>
>
>
>
>     Whether "about half" is good enough does depend where the
>     frontrunners are in each voter's ordering of candidates, but given
>     that the frontrunners are likely to be close to the median across
>     all voters anyway, then they will likely be positioned near the
>     median of most voters' ordering.
>
>
>         c) But you needn't bother with a) or b).
>
>         Even without strong top & bottom-sets, you can still take a
>         guess about which set you'd like to elect instead of the other
>         candidates.
>
>
>         Maybe, though you don't have strong top & bottom sets, you
>         have _ordinary_ top & bottom sets, meaning that the merit
>         difference between the sets is greater (even if not
>         incomparably greater) than the merit differences within those
>         2 sets.
>         If so, you likely will feel like approving (only) all of your
>         (ordinary) top-set.
>
>         Or maybe even that isn't so, and you don't have any kind of
>         top & bottom sets. Maybe the merit gradation is uniform,
>         without any gaps or natural dividing-lines. What then?
>
>         Well, then you don't know where to make your approval cutoff.
>         You don't have an obvious way to choose which set you want to
>         approve over the other.
>
>         No problem! If you don't know which set approve, then it
>         doesn't matter!
>
>         Just approve as you feel like. Maybe just guess. Maybe flip a
>         coin, or draw a number from a bag. Or have the candidates'
>         names in a bag, and draw one to choose which one to approve
>         down to. If you don't know which set you want to approve, then
>         it doesn't matter which set you approve.
>
>         Any such set that you choose by guessing will include the
>         best, and won't include the worst, and will be within the
>         range that you feel that the approval cutoff should be in.
>         That's good enough! Don't worry about it.
>
>         Another thing: If, by guessing or drawing from a bag, you make
>         a choice of what set to approve, but, when you start to
>         actually do so, you don't feel good about it, then don't do it.
>
>         Maybe you'll say to yourself, "This is _disgusting_ !"   Then
>         of course don't do it. Don't approve down that far. Go by your
>         feelings.
>
>         People who assume, as a starting premise, that it's necessary
>         unnecessarily difficult for themselves. Even the more
>         elaborate methods, the ranking-methods, do do that as
>         reliabliably automcatically as their advocates sometimes seem
>         to believe.
>
>         top-set, or (absent either of those) a set that is a good
>         guess, within the range where you feel that the approval
>         cutoff should be--By approving that set, you're maximizing the
>         probability of electing from that set.
>
>         And that's good enough.
>
>         My message to those who complain that Approval doesn't
>         automatically elect the best candidate that you can get is:
>         You worry too much.
>
>
>     I'm not so worried about electing the best.  I would worry about
>     electing a much worse candidate in a surprising upset.
>
>
> Then, in Approval, approve all of your strong top-set.
>
>     Elections really ought to be much more boring, but not enough to
>     put us to sleep.
>
>
> With honest elections and honest media, elections wouldn't be boring,
> because you'd be choosing among various versions of the very best. The
> choice among them, the discussion regarding their different approaches
> to the best policies and directions, would be anything but boring.
>
> What's boring is when the media keep claiming your choice is between
> two criminallyi-corrupt, bought candidates, and when people believe it.
>
> Michael Ossipoff
>
>
>
>
>         Michael Ossipoff
>
>
>     I'm still planning to reply to a couple of your earlier messages
>     with a couple more comments.
>
>
>     --
>     Daniel LaLiberte
>     daniel.laliberte at gmail.com <mailto:daniel.laliberte at gmail.com>
>
>
>
>
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