[EM] Notes on a few Later-no-harm methods

[Richard Lung]

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
>>     ----
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>>
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