[EM] Notes on a few Later-no-harm methods
Richard Lung
voting at ukscientists.com
Thu Jun 2 10:10:09 PDT 2022
On 02/06/2022 11:28, Richard Lung wrote:
>
>
> Sometimes the keep value quotient, in binomial STV, does not help to
> decide an election. It may even make the contest less decisive. Never
> the less, the quotient is an extra source of rational information, to
> that provided by the quota, as to the decision or indecision of the
> public.
>
> The simple plurality method generally implies, representatively, that
> it should not be in a single-member system, but at least in a two
> member system, and often in a three or four member system.
>
> Likewise, I recommend a minimum of a 4 or 5 member system for binomial
> STV, for sufficiently representative elections, to produce decisive
> results.
>
> The draft Scottish constitution recommended a minimum of four member
> STV constituencies. The Irish constitutional convention recommended a
> minimum of five-member STV constituencies.
>
> The McAllister report on the Welsh Parliament cited an academic
> consensus on four to seven member constituencies for sufficient
> diversity of representation.
>
> Four Welsh reports have recommended the single transferable vote.
>
> Thus, a lack of decisiveness, in single-member binomial STV, is not
> necessarily a problem of BSTV but it is a problem of single, double
> and even triple member constituencies. The insistence on a decisive
> election winner is a presumption of social choice theory.
>
> The incompleteness theorem of Kurt Gödel is not an insistence on the
> “Impossibility” of deductive science. It took the theorem of Kenneth
> Arrow to assert that for logical democracy. (The assertion, that no
> election method is perfect, is not a scientific statement, and can be
> disregarded as such.)
>
> A first principle of the philosophy of science is not to presume what
> one is supposed to be trying to prove. The search for knowledge
> requires that ones assumptions may be disproved.
>
> What elections demonstrate, from the irrational simple plurality
> count, to the rationalistic binomial STV, is that popular opinion may
> be indecisive. There may be no demonstrable winner.
>
> What first past the post does do is to provide an administratively
> convenient decision, rather than a necessarily popular decision.
>
> Meek method also incorporates a help to the returning officer. Quota
> reduction with exhausted preferences makes for less equitable
> placements, but facilitates election to the final seat, in the
> multi-member constituency.
>
> Thus, the impossibility theorem insistence on decisive results amounts
> to an imperative for an administrative decision, and not necessarily
> popular representation. But the United Statesis a republic, a thing of
> the people, not a thing of Administration, or a “rebureau.”
>
> Regards,
>
> Richard Lung.
>
>
> On 31/05/2022 01:29, Forest Simmons wrote:
>> Kristofer noted in passing a very important and under-appreciated
>> advantage of Condorcet methods:
>>
>> It can be shown that, for methods where a majority can always force
>> an outcome by coordinating how they vote, then modifying the method
>> so that it elects the Condorcet winner if there is one never
>> increases the proportion of elections where strategy is useful, and
>> may indeed reduce it.
>>
>> This is a good reason to routinely include in the description of
>> every Universal Domain single winner method that satisfies the
>> Majority Criterion, verbiage to the effect ...
>>
>> "Lacking a candidate that outranks any opponent on more ballots than
>> not ..."
>>
>> -Forest
>>
>> El sáb., 28 de may. de 2022 9:43 a. m., Kristofer Munsterhjelm
>> <km_elmet at t-online.de> escribió:
>>
>> On 24.05.2022 21:05, Richard Lung wrote:
>> >
>> > The snag is that these and other criteria were invented for what
>> > amounts to uninomial elections, that is elections that don't
>> have both,
>> > or either, a rational election count and a rational exclusion
>> count.
>> > Together they make possible the application of the binomial
>> theorem, to
>> > higher order counts. My binomial STV hand count is just a first
>> order
>> > binomial count of one election count and one exclusion count.
>>
>> The criteria are method-agnostic: for any ranked voting method
>> (in this
>> case, that supports truncation), if someone gives you a failure
>> example,
>> you can verify if the method passes or fails the criterion without
>> knowing anything about the internals of the method.
>>
>> Put differently, suppose that in a scenario perhaps reminiscent of
>> Roadside Picnic, a mysterious device falls out of the sky. And it
>> turns
>> out that this mysterious device calls elections: you can input ranked
>> ballots with a set of buttons and get the results shown as a
>> series of
>> lights on the other end.
>>
>> Then as long as it allows for ballots with truncation, it's
>> possible to
>> check if a particular ballot where A-first voters truncate can be
>> used
>> to induce a later-no-harm failure.
>>
>> Whether the strange technology that makes up the device implements
>> rational election and exclusion counts doesn't matter. As long as
>> it's a
>> ranked voting method outputting winners and supporting
>> truncation, the
>> question "does this pass later-no-harm?" makes sense.
>>
>> The same goes for things like monotonicity, participation,
>> consistency,
>> Smith, Condorcet, etc. The criteria say something about the desired
>> behavior of a method. Nothing about the inner workings makes the
>> criteria inapplicable (apart from some exceptions like the polynomial
>> runtime criterion).
>>
>> Without a mathematical description of the method, you couldn't be
>> sure
>> it actually passes later-no-harm or later-no-help, but as soon as you
>> found a counterexample, that would settle the question in the
>> negative.
>>
>> > I am not aware of any untoward effects of tactical voting on
>> the bstv
>> > system. I am aware of it doing away with residual
>> irrationalities to
>> > traditional stv, including Meek method. Tho I accept that
>> traditional
>> > stv (zero-order stv in relation to binomial stv) is a robust
>> system,
>> > in practise, as the Hare system of at-large stv/pr.
>>
>> As a ranked method, it must fail IIA, which means that strategy must
>> sometimes be possible. And as it fails Condorcet, the obvious
>> starting
>> place to look is for an election where it doesn't pass Condorcet. For
>> instance, this:
>>
>> 549: A>B>C
>> 366: B>A>C
>> 366: B>C>A
>> 366: C>A>B
>>
>> A is the Condorcet winner. The first preferences are:
>> A: 549, B: 732, C: 366
>> and last preferences:
>> A: 366, B: 366, C: 915
>>
>> so the ratios are:
>> A: 366/549 = 0.67
>> B: 366/732 = 0.5
>> C: 915/366 = 2.5
>>
>> so B wins. Then the C>A>B voters have an incentive to vote A>C>B
>> instead
>> (compromising), after which the counts are:
>>
>> A: 366/915 = 0.29
>> B: 366/732 = 0.5
>> C: 915/0 = infinity
>>
>> and A wins. The C>A>B voters prefer A to B, so the strategy is to
>> their
>> benefit.
>>
>> It can be shown that, for methods where a majority can always
>> force an
>> outcome by coordinating how they vote, then modifying the method
>> so that
>> it elects the Condorcet winner if there is one never increases the
>> proportion of elections where strategy is useful, and may indeed
>> reduce it.
>>
>> > BSTV counts require values for all preference positions, which are
>> > equal to the number of candidates. Any preference position may
>> be an
>> > abstention. A citizen who never voted but made an exception of
>> their
>> > dislike for Donald or Hilary could abstain on their first
>> preference
>> > but vote for either on their second preference, effecting an
>> > exclusion, because there is only one vacancy.
>>
>> > That is the theory of it. I don't know how well it would work in
>> > practise, because there never has been a practise. But I do
>> know that
>> > democracy is minimised, and evidently works badly, based on single
>> > vacancies, in the Anglo-American systems.
>>
>> > Fully fledged binomial stv, FAB STV, does not work on less than
>> 4 or
>> > 5 member constituencies, the minimum requirement for a democracy of
>> > all the people being represented by their choices.
>>
>> > Thank you for your examples. They have helped clarify my
>> thinking -- somewhat!
>> > According to my (accident-prone) working, A wins on a keep
>> value of 38957/58966.
>> > B also has a less than unity keep value of 38957/39366. The
>> > difference is that one can say A has been elected on a quota of
>> > 48961.5, with 58966 first preferences.
>> > But B has not reached the elective quota. Tho B has not reached the
>> > exclusion quota, that only says B has not been excluded.
>>
>> So by the keep values: A's first preference count is 58966 and last
>> preference count is 38957, since the keep value is 38957/58966.
>>
>> You say that B's keep value is 38957/39366, i.e. first preference
>> count
>> of 39366 and last preference count of 38957. But that seems to be in
>> reverse order. Indeed, your HTML page shows that it is 39366/38957.
>>
>> >From the keep values, it seems that truncations are not included
>> when
>> counting last preferences. I was pretty sure that BSTV would fail
>> later-no-harm because the standard way of counting truncations,
>> as STV
>> does, is to consider everybody not ranked to be equal-ranked for
>> last;
>> and if you had done that, then it would be possible to induce
>> later-no-harm.
>>
>> The good news is that you avoid this particular problem if you count
>> anything past truncation simply as abstentions. So I guessed wrong,
>> which was then cleared up by the example, which shows how useful they
>> are :-)
>>
>> However, instead it seems that you get later-no-*help* failure.
>> Consider
>> this modified election:
>>
>> 18125: A
>> 20035: A>B>C
>> 18722: A>C>B
>> 34488: B>A>C
>> 38634: C>B>A
>>
>> By my count, the first preferences are: A: 56882, B: 34488, C: 38634
>> and the last preferences are: A: 38634, B: 18722, C: 54523
>> and the last to first ratios are: A: 0.68, B: 0.54, C: 1.41
>>
>> so B wins. But if now the A voters fill out their ballot by voting
>> A>C>B, then B's last preference count changes to 36847 and A wins
>> instead. This is a violation of later-no-help.
>>
>> Ordinary STV passes both.
>>
>> I should note that Condorcet methods, that I prefer, fail both.
>> My point
>> isn't as much that later-no-harm and later-no-help are intrinsically
>> good, as that it's much easier to check a claim by concrete evidence
>> than by references to personal terminology (which may be hard to
>> understand for others or take a lot of time to get acquainted with).
>>
>>
>> On a final note, I would say that always counting truncation as
>> abstention could lead to an unknown candidate problem: suppose
>> there's a
>> candidate who nobody has heard of and thus nobody bothers to
>> rank. But
>> he has a dedicated following all of whom rank him first. If nobody
>> obtains a majority, then this candidate could win, e.g. something
>> like:
>>
>> 3300: A>B>C
>> 3300: B>C>A
>> 3200: C>A>B
>> 2: D
>>
>> I'm also not entirely sure what's going on with the quota
>> transfers. If,
>> in the single-winner case, someone who exceeds the quota is
>> automatically elected, then there's no need for any transfers.
>> However,
>> if passing the quota doesn't guarantee victory, then later-no-harm
>> failure might actually be possible. Suppose A is just above the quota
>> and B is just below it (with B closer to the majority line), then
>> if the
>> A voters only vote for A, A might win; but if they vote A>B, then the
>> surplus might be transferred to B and make B win. Perhaps. As I said,
>> I'm not sure how the logic works in that case.
>>
>> -km
>> ----
>> Election-Methods mailing list - see https://electorama.com/em for
>> list info
>>
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