# [Election-Methods] YN model - simple voting model in which range optimal, others not

Dave Ketchum davek at clarityconnect.com
Sun Mar 30 19:27:36 PDT 2008

```On Sun, 30 Mar 2008 12:54:40 -0400 Sun, 30 Mar 2008 12:54:40 -0400 Abd
ul-Rahman Lomax wrote:
> At 08:30 AM 3/30/2008, Dave Ketchum wrote:
>
>>On Sat, 29 Mar 2008 23:28:22 -0400 Abd ul-Rahman Lomax wrote:
>>
>>>At 03:32 PM 3/29/2008, Dave Ketchum wrote:
>>>
>>>
>>>>Some see forest; some see trees; who sees all?
>>>
>>>Those who see a forest made up of trees.
>>>
>>>
>>>>Looking at the 31 voter Plurality example:
>>>>     16 voted for candidates with 3 or more Ys - but NONE for 4 Ys.
>>>>     9 voted for candidates with 3 or more Ns - 9 going all the
>>>>way to 4 Ns.
>>>>
>>>>Seeing that as unbalanced, I inverted it.
>>>
>>>Which, of course, does nothing. Y and N are arbitrary. In the
>>>example, Y means the majority position. Period.
>>
>>Except, with complete inversion, N inherits majority position.
>
>
> (by the way, you meant to write *5* going all the way....)

Ouch!  More carelessness.
>
> Yes. All you have done is to change the names of things. N is now the
> majority position. And YYYY wins. Your point?
>
> The point is that Plurality is a method which considers only first
> preference. If voters vote sincerely, all that matters is that first
> preference, and it is entirely possible (and rational, though not
> "probable*) that there are more first preference voters with the
> majority-rejected position than for any other. Start to consider
> mixed sincere/tactical voting and it gets even more possible.
>
> Plurality only works as a voting method when the field is restricted,
> and, even then, as we know, it can fail. With many candidates, it
> thoroughly breaks down. Range works well with many candidates.
> However, "works well" is still relative. Single-ballot election
> systems with many candidates are inherently flawed; natural systems
> would break the decision down and deal with it hierarchically.
> Hierarchical systems may tend toward the Condorcet winner; however,
> in practice, in the biological applications, decisions are weighted
> and passed on, up the hierarchy, as weighted, thus both Condorcet and
> Range aspects are functioning.
>
> (Note that basic democratic process is hierarchical. Decisions are
> broken down into a series of Yes/No votes. "Election methods," which
> break this pattern, are so problematic precisely because they deviate
> from this practice. There still remains the basic Condorcet vs. Range
> problem; but functional systems do incorporate preference strength
> measures and thus move what might otherwise be accidental (or
> designed) victories for particular members of a Condorcet cycle
> toward the Range winner. In pairwise contests, a weak preference
> attracts little campaign funding....)
>
> (My view is that if it is average Range as distinct from sum-of-votes
> Range, it has somewhat similar problems when there are many
> candidates, and the "quorum rule" is an arbitrary fix that likewise
> can break down with many candidates. Unlike basic Range voting, which
> is quite solid and has been extensively studied with simulations (and
> the simulations had no "abstentions" if I am correct), average Range
> has not been studied and is merely an idea that can seem good at
> first sight. It is a radical departure from existing practice, and,
> if included in Range proposals for real elections, will *kill* them.
> It has a place in advisory systems, where the use of average rating
> is then subjected to further judgment, thus covering all the nasty
> possibilities without trying to create a rigid rule.)
>
>
>>Agreed ANY collection of voters would be possible, but YN offers
>>this collection as demonstrating what to expect from Plurality.
>
>
> No. That is the basic error Dave made from the beginning. "What to
> expect" from Plurality is a gamut of behavior. The example was
> designed to show a bad element of that gamut. Not to claim that this
> is what to "expect."

So we disagree.
>
> With many candidates, though, failure to elect YYYY becomes the norm.
> Election of NNNN would still be rare.

Perhaps not.  Since Plurality reports EXACTLY what voters say, votes might
be more scattered with more candidates.
>
> Consider, though, that if on each measure the electorate is divided
> equally (almost) between Y and N, and if these positions are
> uncorrelated, the pattern described becomes, with many voters, about
> as likely as any other pattern. (That's my intuition. It may not be
> exactly true. But for NNNN to have 5 votes more than YYYY is almost
> as likely as for it to have 4 or any other small number. The
> distribution would be relatively flat around that peak.)
>
>
>>Actually Plurality is neutral as a method - a desirable feature.
>
>
> Sure. So is flipping a coin. Is that desirable?

But Plurality does not flip coins.  Those manufacturing examples may do
such, but Plurality simply reports what is given to it.  In actual
elections whatever influences voters affects their votes and thus what
Plurality has to report.

Some other methods, such as IRV, do interesting manipulations. worth studying
>
> Another neutral method, actually better than flipping a coin, is
> Random Ballot, used with a plurality ballot. A ballot is selected at
> randon and the candidate on that ballot wins. It is actually a
> reasonable method. It *usually* selects the best winner. It behaves
> quite like Plurality in certain ways. But, obviously, it can fail
> spectacularly.

Let's argue this one another day.
>
> The Plurality failure in the example given isn't as spectacular as it
> might seem, because the electorate is actually close to balance.
> Range shows that the balance isn't as close as it might look -- the
> Range margin isn't small -- but from other measures, the result is
> not as bad as it might seem. As much as I detest the result of the
> 2000 U.S. Presidential election, all the violations of law and
> precedent, it must also be seen that the electorate was close to
> balance. It's not as extreme as what is theoretically possible. (IRV,
> as an example, can elect a candidate who is opposed by two-thirds of
> the electorate, as shown by the votes, compared to another candidate.
> That's pretty bad. It's also pretty unlikely to approach that
> extreme, but milder examples probably occur (or would occur if
> top-two runoff is replaced with IRV, as is happening in the U.S.)
>
I would argue against IRV and top-two runoff another day.
>
>>Plurality's inadequacy, which causes us to look for better methods,
>>involves limiting approval to a single candidate.  When faced with
>>candidate collections such as Bush/Gore/Nader, voters sometimes wish
>>to approve more than one as better than those they want to reject.
>
>
> Yes. Approval actually brings us back, closer, to standard
> deliberative process. It holds multiple simultaneous elections. Now,
> suppose that, with Approval, a runoff is held whenever there is
> majority failure, and let's assume that there are two kinds of
> majority failure: no candidate gets a majority, or more than one
> candidate gets a majority. (We should be so lucky as to see the
> latter; in spite of this being a major argument made against Approval
> --- when this happens, it could be that the majority favorite has
> fewer votes than another also-approved candidate, thus the Majority
> Criterion fails --, in real, contested elections, it is quite
> unlikely. It would require a significant number of voters to, say,
> vote for both Gore and Bush. Yeah, right.)

This paragraph is too complex for simple, yet meaningful, response -
perhaps another day.

Approval, itself, is trivial improvement for trivial effort.  Its major
failing is possible acceptance as a destination rather than a step toward
such.
>
> If a runoff is held in either of these two situations, there is then
> the problem of who makes the runoff. The method is quite good with
> simply top-two. However, standard deliberative process, which uses
> repeated balloting to find a majority winner, with *no* candidate
> eliminated (and which can thus go to *many* polls), would indicate
> that this could be restrictive. Still, if we are choosing between two
> candidates, say, both of which were majority approved, the result is
> not going to be truly bad no matter how it turns out.

Runoffs main value is recovering from a methods weaknesses until something
can be done about the method.  They are too expensive to be accepted as if
a normal part of a usable method.
>
> But Approval is also a blunt instrument, still. The method gains
> flexibility if fractional votes can be cast, thus allowing the voter
> to express true preferences *and* preference strength, and then the
> method can actually maximize what Clay Shentrup first called, as I
> recall, Total Voter Satisfaction. If voters vote sincerely. If they
> don't, the method obviously cannot maximize their overall
> satisfaction; however, it appears that it generally fails to do so in
> a direction *not* favorable to those who exaggerate. Exaggeration
> *may* help such voters elect their favorite, but only when that
> favorite is close to winning anyway, and it can help to defeat the
> second choice of those exaggerating voters, and the punishment can be
> quite a bit more severe than the reward.
>
> When Range allegedly disappoints "sincere voters" due to the "greedy
> tactics" of others, the fact is that the disappointment is small. In
> the examples I've seen, those sincere voters will be, as they
> expressed, quite happy with the outcome, and it would only be an
> insinuating voice that would say, "But, if you had exaggerated like
> they did, you'd have ended up with \$1.00 instead of \$0.99." Given
> that my loss of \$0.01 -- multiplied by all those who voted like me --
> was more than balanced by a net gain of my neighbors, I'd tell that
> voice to go fly a kite. And if it was a politician saying that, he or
> she would never again have a chance to win my vote.
>
> Plurality works under current conditions, most of the time, because
> generally the candidates have been vetted so that the choice is
> really between two. Duverger's Law. Plurality creates a two-party
> system. When third parties arise, though, Plurality starts to break
> down. Top-two runoff works *much* better than Plurality (for the same
> reasons as IRV, but with an additional factor that actually makes it
> better than IRV. TANSTAAFL, though. Top-two can cost more; it's not
> surprising that a superior election method would cost more. Approval
> gets us closer at no cost, and Approval plus top-two (which would be
> less common, since Approval helps reach a majority) is a good
> compromise. Bucklin, even better, because it does allow expression of
> preferences. (Three, in the Duluth implementation, with multiple
> approvals allowed in the third rank. I would simply allow multiple
> approvals in all ranks. Thus if you are actually happy with two
> candidates as winners, you can vote for both in first rank.)

Plurality thinking satisfies most voters most of the time.  What makes
sense if the method can be made to fit is, for any election:
Voters satisfied with Plurality thought can vote with ZERO extra
effort imposed by the method.
Voters wanting to express more complex thought can do this with
minimum effort needed to express such thought.
>
> Bucklin has started to seem to me as even better than Approval for
> U.S. practical implementations, though we can get to Approval with no
> cost at all. Bucklin does require more ballot space, though, like
> Approval, it can be done with all existing equipment. With
> hand-counting, it could also be counted in rounds, like IRV, so it
> does not raise hand-counting costs unless it is needed. (But I'd
> still want to see all the votes counted; the common IRV practice of
> ceasing counting when a winner has been found makes it impossible to
> analyze what happened, and to discover and measure IRV majority
> failure -- where a majority preferred another candidate to the IRV winner.)

No comment on this method here.
>
> Bucklin really deserves more attention. Consider that it was popular
> in the U.S. for a time, and consider that it was working. Arguments
> against it were not based on actual harm that made sense. My theory,
> as yet unsubstantiated, is that it was outlawed or rescinded
> precisely because it was working, and it would have allowed third
> parties to gain a toehold.
>
>
>
>
>>I object to calling this example "likely" - think of such as 16 with
>>3 Ys together with ZERO 4 Ys.
>
>
> Yes, but. Think of 100016 with 3 Ys together with 100000 with 4 Ys.
>
> That is, add 100000 to all position counts and thus to all vote
> counts. The results are the same. It looks drastic because the
> election has been boiled down to the *margins*.
>
> Note that if positions are random, we would expect 4 occurrences of
> 3Ys for every occurrence of 1 Y. It is like the number of occurrences
> of coin toss patterns. If we throw a coin many times, and count the
> occurrence of each sequence of four, we will get these patterns of
> equal probability:
>
> YYYY
> YYYN
> YYNY
> YNYY
> NYYY

Without arguing the exact validity of the above, the following
combinations in the test case were stretching expectability:
16 3Y with 0 4Y
4 3N with 5 4N

And, again, Plurality did not fail - it simply responded neutrally to the
>
> There are four of the 3-match positions to each one of the 4-match.
> Actually, what is unlikely is that there are so many NNNN positions,
> and, in the expanded situation I mentioned (add 100,000) to all
> votes, that there would be so *many* YYYY positions and NNNN
> positions is the oddity, not that there are so few.
>
> But these were *not* random positions. They were chosen to show a
> behavioral extreme. Yet Range functions fine with that extreme.
> That's the point. Plurality breaks down, IRV performs okay (choosing
> a 3Y candidate in that situation), but Range performs perfectly,
> because it was, in fact, designed to. So does Bucklin, so does
> Approval (probably).
>
>
>>>However, not only does it seem probable that Dave would not
>>>understand this, I'd guess he is not reading this at all, because
>>>he hasn't responded to any of my explanations, only to Warren. So,
>>>would someone who isn't filtered out by Dave be so kind as to
>>>explain this to him?
>>
>>Tracing the filtering back to what you sent me on 23/3/08 at 2359, I
>>assume it was unintentional, and will undo it.
>
>
> I've looked at my email records and find nothing that would explain
> this comment. Perhaps someone can help us out. To my knowledge, I
> sent no comments personally to Mr. Ketchum, but only replied to
> "All." Mr. Ketchum's copy of that mail would have the original
> headers, I assume. If he sends them to me personally, I'll examine them.
>
Will send.
>
>>I did not attempt to analyze the quality of the Range analysis, but
>>suspect that, based on what was done to Plurality.
>
>
> An example was presented where Plurality does maximally poorly, Range
> performs like it always performs, to maximize expressed voter
> satisfaction. Range would perform this way with *all* election
> scenarios. Now, how often would Plurality choose the YYYY winner?
> (i.e., over all possible permutations).
>
> You can estimate it from the relative frequencies. Plurality with
> sincere voting (one of the conditions) will choose the specific
> candidate with the most voters matching that position. As the
> situation is designed, all the specific positions would have the same
> probability. (This is equivalent to saying that every exact sequence
> of coin tosses has the same frequency as every other exact sequence.
> There are four times as many 3Ys as there are 4Ys because the latter
> is an exact sequence and the former is comprised of four different
> exact sequences.)
>
> Thus Plurality would choose YYYY one out of sixteen times.
> It would choose one of the 3Y candidates four out of sixteen times.
> It would choose one of the 2Y candidates six out of sixteen times.
> It would choose one of the 1Y candidates four out of sixteen times.
> It would choose NNNN one out of sixteen times.

One more time:  Plurality reports what the voters vote.
>
> However, Range would always choose YYYY. It was *designed* to do that.
>
> Always. If voters vote sincerely.
--
davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
Do to no one what you would not want done to you.
If you want peace, work for justice.

```