Liberating democracy from Impossibility Theorem.

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Arrow theorem of “no best voting method.”

The non-monotonicity condition.

Mistaking an improbable contingency for a logical fallacy.

Tactical total war: 2015 UK general election as exclusion campaign, as exclusion campaign.

Non-monotonic gaming with first past the post.

Other Arrow theorem conditions.

Ill-chosen rules for judging election methods.

Inconsistent rules for logical election methods.

Arrow theorem of “no best voting method.”

Researching voting methods on the web, I was a little surprised to be frequently assured that there is no best electoral system. It soon became apparent that the bedrock of this assurance was a theorem by Kenneth Arrow. A school, known as social choice theory, adapted this so-called Impossibility theorem, as a rock upon which foundered every ship, considered as all the different kinds of voting methods.

This alleged anarchy of voting methods is not as rock-solid, as appears at first sight. A typical assertion of this law of anarchy is: “There is no perfect voting system.” This seems a safe position to hold but it actually is an empty claim, as far as implying “there is no best voting system.”

A more slippery or ambiguous version reads: “There is no single ideal voting system.”
That could be interpreted to mean either no “perfect” or no “best” system.

Well, we will have to see for ourselves.

A theorem is a mathematical device to prove certain propositions. The classic model is Euclid geometry. This consists of a few basic assertions, originally regarded as self-evidently true, the consequences of whose inter-relation derive further propositions. Their logic may be regarded as proof. Moreover, their truth may be independently tested by checking with evidence, designed to disprove them, if possible, as general rules.

Arrow theorem follows this model (tho it follows in the foot-steps of Godel incompleteness theorem). The theorem states a few basic rules, believed must apply for any voting method to be comprehensively logical. A proof was forthcoming that no voting method that did or could exist satisfied all these principles.

Well, you can’t argue with logic. And it seems that many people accept this state of affairs as unshakeably as believers in the catechism. This academic insistence, that there is no best election system, has been particularly helpful to politicians thriving on broken voting methods.

It hasn’t done democracy any favors tho. “No best voting method” has become an apology for the world anarchy of largely ineffective voting methods, not to mention a correlation of world apathy towards ineffective politics.

The non-monotonicity condition.

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Before looking at all the Arrow theorem first principles or axioms, let us just look at how one of these basic rules has been applied to discredit the best voting method. Many experts, political scientists and reformers, regard the single transferable vote (STV) as the best system. But Arrow theorem finds that it is not “monotonic.” This claim was eagerly seized on by the Plant report, which recommended the Supplementary Vote.

'While the Plant Report rejected STV on the grounds of monotonicity failure, it was “particularly galling” that the Report recommended “the very inferior SV, that contains the very same fault as that for which they rejected” STV (Hill, 1994). (This point seems unanswerable.)'
[Nicholas R Miller 2002.]

In this context of elections, “monotonic” is fancy mathematical jargon for a certain kind of tactical voting, or strategic voting, as it is known in North America. It happens in exhaustive ballots, excluding the candidate with the least votes in a round, so that their votes may be re-distributed to his voters next choices.

“Non-monotonic” tactical voting may occur when a leading candidate does not want to be in the final round with a candidate, of wider appeal, who is currently runner-up. So the leaders supporters transfer just enuf of his votes to give a trailing candidate, of narrow appeal, more votes than the runner-up. This way, the runner-up is pushed into third place and excluded for the final round.

In real life, this kind of tactical voting may happen when a center candidate comes second, and has a left wing and a right wing candidate on either side of him. The wing candidate, in the lead, knows that if the opposite wing candidate, in third place, is excluded, then most of those excluded candidates next preferences will go to the center candidate, thus given the final lead and victory.

In 2013, Michael Gallagher gave a paper on “monotonicity and non-monotonicity at PR-STV elections.” He reckoned non-monotonicity could have taken place in 20 of 1326 Irish elections or 1.5%. These actually included the alternative vote (AV) as well as STV. The incidence for size of constituencies was not given.

These are only theoretical potentials for non-monotonicity. In fact, the voting information simply isn’t available till after the election count itself. (And then, not the ballot papers of voters preferences.) Indeed, on this, Gallagher based his research.

The potential was there but the realisation was not. This crucial distinction was rather over-looked, in glibly speaking about non-monotonic elections, which are nothing of the sort.
The Northern Ireland returning officer, who said as much, and knows a thing or two about STV elections, was probably right.

Gallagher only gives one real example, and that is only of a nearly possible non-monotonicity. And this was no more than a rumor showing the game was understood. It was not put into practice and it did not need to be put into practice to make any difference.

This example was in the penultimate round of the 2005 exhaustive ballot for the Tory leadership. David Cameron was on 90 votes. David Davis on 57 votes. Liam Fox on 51 votes.

Respectively, this was a Tory left, center, right line-up. In practise, this is the typical scenario for non-monotonicity. It was rumored that some Cameron supporters might shift enuf of their votes to Fox, so that Davis was excluded with the least votes. Some Davis voters next preferences would go to Cameron but most Fox voters next preferences would go to Davis.

For some Cameron voters to shift to Fox would have been insincere or tactical voting, to game the system. Such would be false voting.

Now look at this from the point of view that the system is non-monotonic. The complaint is that the leading candidate gains votes from a runner-up, who thus falls into last place and is excluded, instead of another rival.
The next preferences of the newly excluded candidate are less favorable and only serve to make the leading candidate lose his lead, instead of win in the final round.

Gallagher quotes some of the critics going into hysterics against STV, as the agent of sin and chaos, for supposedly depriving a candidate of election by his getting more votes.

Now look again at this situation, in the real life context of that Tory leadership contest. A Cameron, on the left, is not likely to gain votes from a Fox, on the right. People don’t vote like that. The scandal of the “non-monotonic” eventuality is unreal. It does not resemble how people follow their perceived interests.

The greater likelihood is that the apparently unjustly deprived leader is a party to depriving the more widely acceptable rival. The supposed victim is more likely the villain. So much for the hysterical critics of “non-monotonic” STV.

Mistaking an improbable contingency for a logical fallacy.

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The critics for monotonicity, so-called, have mistaken a wobble in the system for a logical fallacy, when it is merely a contingency. Judging by the few times Gallagher found it and judging by the political alignment it requires to operate, like an alignment of the planets, perhaps it is not a very realistic contingency, at that.

A non-monotonic alignment is treated by critics in superstitious awe of this herald of electoral catastrofe. Far from being a precursor of chaos, voting patterns are structured. Winning votes to lose, instead of win, merely may mean the difference of not competing or competing with a more generally accepted candidate or Condorcet winner.

The real issue is whether the leading candidate does or does not have the Condorcet winner for a straight fight. Whether or not he gains votes, in the process, is irrelevant to this over-riding factor.

O B Gordon suggests a probable means of improving the chances of the Condorcet winner not being excluded early in an STV election. Instead of starting the count with the usual Droop quota to elect to a certain number of seats, he adjusts the quota, so that it elects all but one of the candidates with the least votes, in successive rounds. He calls this modification Exhaustive STV (ESTV).

I’ve suggested it myself, tho not for this reason, which I think is rather good, working on probabilities, as it does, which is what election results are.

Non-monotonicity, as conceived in terms of election systems, is not the strictly logical necessity it is in mathematics. Rather it is a contingency or happenstance, that does not preclude a saving logical reason for it happening.

Elections are not axiomatic systems, which can only treat fluctuations in the preference data, as errors of deduction. Rather, counts, more or less, aggregate the individual voters preferences to an approximate community preference.

The only example, Gallagher gives, is only of a near potential for non-monotonic voting, not actual non-monotonic voting. Moreover, the voting system is not STV, nor even AV. It is the exhaustive ballot. And the peculiarity of exhaustive ballots for the party leaders is that the voters are given time to look at the results of each stage of the count, before deciding how they will vote next.

That was how it was possible for Tory MPs to even consider gaming the system in a non-monotonic fashion. That is the point. They had the time and information and organisation to effectively rig the result, with no possible electoral counter-measures available to their opponent.

This particular voting system of a staggered exhaustive ballot offered some Tory MPs an ideal opportunity for non-monotonic gaming. Yet thru honesty and prudence and whatever other reasons, they chose not to do so. Perhaps they’d divined the final outcome that there was no need for tactical voting.

None of these ideal conditions are available for preferential voting systems and decreasingly so for STV in increasingly multi-member constituencies, with their complexity of possible preferences between all the candidates. Put yourself in the candidates position and you can see that non-monotonic gaming would be a pointless gamble.

We cannot say for certain that it never happened. We can be reasonably sure that if any candidate was tricked out of a seat in this manner, his campaign would sense that something was going on and be sufficiently aggrieved to speak out.

You only have to look at a comparable instance of an Irish government gerrymandering the boundaries of three or four member constituencies. The press commented that the minister responsible nearly gerrymandered himself out of the Dail.
Subsequently, an independent boundaries commission was established.

Tactical total war: 2015 UK general election as exclusion campaign.

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Non-monotonicity is claimed to be a failing of systems with preference voting and exclusion counts. But these properties are implicit in first past the post (FPTP). The admonition to vote tactically or strategically means that a voter is expected to vote for a candidate, who is less than his first preference. That means most voters have, in their minds, an order of preference for various candidates. It is just that the x-vote only establishes a single preference, not necessarily the first choice of candidate.

The admonition, blackmail or arm-twisting, against wasted votes, effectively tells (extorts) voters to exclude candidates, they most prefer, because they have the least support.

Thus, FPTP implicitly contains a preference exclusion count. Some FPTP voters are effectively blackmailed into being their own returning officer by re-distributing their higher preference to a lower preference and excluding the higher preference from the count.

This preferential deprivation applies to a whole nation under the thrall of first past the post. Perhaps we can take the salient case of the Tory peer Norman Tebbit to make the point. He urged people to vote UKIP (his first preference?) in the British Euro elections.

In the 2015 general elections, Tebbit observed that a Tory vote (his second preference?) for Labour (his third preference?) in Scotland would help keep out the SNP (his no doubt less than fourth preference.)

The 2015 British general election was a seething mass or snake-pit of tactical vote campaigning.

The base-line was set by the manoevring over the line-up of party leaders in television debates.
Premier Cameron refused to accept a one-to-one debate with the Labour opposition leader, which would define him as the alternative premier.

Yet, going round the country, he characterised the campaign as a presidential election between himself and the less popular Ed Miliband. He was reducing the general election to an electoral college for his own primacy. That's quite a constitutional down-grade, of the complex problems of government, to one simplistic binary choice.

The only tv debate Cameron would tolerate was a seven-way line-up with the leaders of Labour, the Liberal Democrats, the SNP, Plaid Cymru, The Greens and the UK Independence party.

Leaving out the Democratic Unionist Party from Ulster/Northern Ireland was telling. (The courts turned down their challenge of the exclusion.) The DUP showing wouldnt affect the Tory party fortunes. Giving an unprecedented showing to three left parties, which were a drain on the Labour vote, suited Tory tactics well.

Ed Miliband even complained to the SNP leader that she was urging an alliance to keep out the Tories, yet urging Welsh voters to support Plaid Cymru and English voters to support the Greens.
Ranked choice or order of preference plainly matters, yet the voting system was left without a preference vote.

Tory premier Cameron urged Liberal Democrats and UKIP supporters to switch to the Conservatives, to keep out Labour, allegedly in thrall to the SNP.
Naturally, for Cameron, tactical voting was only alright to suit the Tory party. The will to win becomes total commitment to manipulating the voting system.

26 April 2015, The Mail came out with the headline, "May: SNP/Lab Pact 'Worst crisis since abdication'
Subtitles, "English voters would 'not accept legitimacy' of an alliance
Poll: Four in 10 Ukip backers will switch to Tories to stop deal"

The May in question was not the month of the election but terrorists-under-the-bed Tory Home secretary Teresa May, who was being quoted (not the English people).

Not meaning to be disrespectful, it might be fair to say I struggled to make out what were the Tory lwnys talking about?

The Mail helped my understanding, with the famous dominatrix poster of Scotlands first minister, holding a whip, while in black lace suspenders. (This homely woman reminds me rather of pastors daughter, Angela Merkel.) Imagine the incredulity of my suspicion that May and The Mail were insinuating that Ms Sturgeon was another Mrs Simpson! Ex-colonials, I suppose.

Well, the ancient Romans had their Saturnale every year, when the slaves were made the masters and the masters made to look ridiculous. The ancient Britons of the Tory party have made sure that they only will make themselves look ridiculous once every five years, in that democratic saturnale, a general election.

This Tory silliness was a serious attempt to push the English to sacrifice their first preferences for Ukip, or who-ever, and donate their X-vote as a second or third preference for the Tories.

On the sunday before polling day, Cameron came out with his UKIP-stopping "red-line" that he would not go into coalition without a commitment to a referendum on leaving the European Union.

The UKIP leader Nigel Farage emphaticly agreed to a reporters question that voters should vote tacticly.

The Liberal Democrats, suffering badly from their broken promises after the last election, campaigned to position themselves as a center party, in effect the Condorcet winner. That is to say a party that might hope to win in seats where they approach a straight fight between either a Labour or Tory candidate. Because, both right and left wing voters might prefer, and vote tacticly for, a center candidate to each other, as their opposites.

In the 2010 election campaign, the Lib Dems posed before a bill-board promise of no tuition fees for students. (They broke other promises of no less import.)
In 2015, Labour exhibited a monolith of six promises signed by Ed Miliband. While announcing this parody of the Lib Dems promise, he denounced Lib Dem leader Clegg for his betrayal.
The "Ed-stone" was conspicuous by what it didnt promise, rather than its vague generalities.

Stuck at a fall from 23% in 2010 to a steadily projected 8% (which came true) the Lib Dem vote was already squeezed dry by defections to Labour. So, it is doubtful there was much more to be gained by Labour targeting the Lib Dems.

The 2015 general election was marked by the unwillingness of the two main party leaders to contemplate anything other than an over-all majority of seats, while they languished in the polls at more or less one-third of the votes each.

The opinion polls prediction of about 34% for the Tories and Labour was about 3% out. Labour won about 31%, an increase of one and a half per cent. The Tories increased their vote from 36.1% in 2010 to 36.9% in 2015, only an increase of 0.8%. The two main parties enjoyed a more or less insignificant increase in support.

Almost all the polls predicted a hung parliament and almost everyone believed them. The Tories got a majority of 12 seats, almost 14% over-represented in seats for votes.
This miscalculation helped to disguise an out-standing fact. Not even the collapse of the Liberal Democrat vote was enuf to more than shore-up the declining trend in support for the two-party system.

The Lib Dems were the new party who set out "to break the mould of British politics," not to mend the mould, as they did after the 2010 election, abandoning their radical policies. The voters broke the Lib Dem mould-menders, instead.
It remains to be seen whether this annoyance with the Lib Dems has diverted the trend against two-party politics.

The erratic simple majority system (First Past the Post) added to its history of audacious misrepresentations. There are signs that the distracted British public finally may run out of patience with its distortions of the truth.

Ukip with nearly four million voters and the Greens with over a million made five million voters represented by a seat each for these two parties. They may share a joint electoral reform campaign platform.

In 2015, the Tories incited tactical voting for themselves but boosted the profiles of Labour support-draining parties. They had also been the prime financers and propagandists (with much Labour help, tho not from their leader) in defeating the Alternative Vote.

It may be surmised that the Tory and Labour unwillingness to discuss coalition and power-sharing will be the real coalition against real reform of the voting system for power-sharing, not just between the parties, but between the whole community with democratic election method.

Early in the campaign, the SNP leader Nicola Sturgeon called for a fair voting system.
The quota-preferential voting method would be the sane response to the tactical total war of 2015.

Non-monotonic gaming with first past the post.

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Even such arcane gaming, as non-monotonicity, took over a news-paper headline, indeed gained main-mast prominence.
Right on the top of their front page, The Mail pictured the SNP leader Nicola Sturgeon, with the caption: the most dangerous woman in Britain.

Sturgeon responded that was the nicest thing The Mail had said about her.
After that, television reported a further surge in SNP support.

Labour leaders, like Alistair Darling, complained that the Conservatives were making too big a thing of the SNP. They were rousing English nationalism against Scottish nationalism and threatening the union.

This objection was more credible, in that Lord Forsyth complained that his party was risking the union by demonising the SNP.

38 degrees e-mail, SNP: behind the media spin, reported some news-papers launching daily attacks on the party, “the right wing media’s worst nightmare.”

The leading party, in parliamentary seats, the Conservatives high-light the probable third party in Westminster seats, inspiring extra votes for them, thru the oxygen of sensational publicity, to ensure they well over-take Labour in number of Scottish seats.

The Mail on Sunday had Sturgeon and Labour leader, Miliband super-imposed on a pose from The Phantom of the Opera. This wasnt too far from the principle: All publicity is good publicity.

The Tory campaign poster was a big picture of Nicola Sturgeon with Labour leader Ed Miliband as a puppet on a string. That is because they would rather make the general election a campaign against the Scottish independence party, the SNP, less liked by the English, than fellow unionist party, Labour.

The Tories generally try to characterise the election as opposing the Left, rather than the center-left, belittled as a puppet. The SNP just happened to be a convenient campaign substitute for the Tories usual left-wing bogey.
And that is the non-monotonic gaming principle.
The Tories are a non-monotonic party!

In 2015, the usual tactical voting campaigns, under first past the post, included this potentially government-changing kind of tactical campaign.
In any case, this is surely a classic vicious circle, of a dishonest voting system addicting to dishonest campaigning and vice versa.

In the sense in which the term, non-monotonic, is used in literature about social choice theory, it has been ascribed as a theoretical possibility with STV. Actually STV makes it an unrealistic gamble. There appears to be no evidence of any case of non-monotonic gaming, to change the result, by so much as a single candidate, in any official STV elections.

Non-monotonicity is a mote-in-your-eye criticism of STV, to excuse a chronic failure to implement democratic voting system.

Maybe the clearest example of the potential for vicious or non-monotonic gaming is to be found in AMS. In 2003, A Welsh Conservative candidate on the party list privately encouraged voters not to vote for his colleague in the single member constituency, to maximise his chances as an Additional Member.
(Changed Voting Changed Politics.)

Other Arrow theorem conditions.

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We move on from non-monotonicity to other Arrow theorem conditions. There are different versions of this theorem, of which I am not a specialist, and only propose to comment on certain aspects, with respect to voting method.

We may remark in passing, that the condition of non-dictatorship (more or less) precludes party list systems, which are more or less dictatorial, because the order, in which the party candidates enter parliament, according to the party share of total votes, is decided by a party boss or caucus or activists.

William James observed a certain blindness in human nature, which the widespread use of these exclusive list systems vindicates.

Take condition, Individual Sovereignty: Each individual should be allowed to order the choices in any way and to indicate ties.

I couldn’t help but feel that the deviser of this theoretical condition didn’t know much about practical elections. “To indicate ties” sounds harmless enuf requirement. Actually, it is not so much a ballot box as a Pandora box.

The total number of possible ordered choices for any given number of candidates is the factorial of that number. This is an astronomical number, which soon becomes impractical to calculate without a computer.

But factorials pale into insignificance, if you take into account all the possible permutations of tied preferences as well. In mathematical fact, the factorial of the number of candidates, indicating all possible preferences between them, is only a small sub-set of all the possibilities including ties, calculated by the multinomial theorem.

Never mind! our supposed grand system building theorist might say. But he should have to mind also the dubious logic of including ties, which are non-elective, in elections. We are not designing predominantly non-elective elections.

If a voter is indifferent towards two candidates, it should not matter in which order he places them. He only has to toss a coin to decide. And if everyone else, in the same position, also makes a random choice, that honest indifference will be reflected in the resulting count.

Human choice has an element of indeterminacy, so that a completely deterministic theorem cannot represent real elections or draw definitive conclusions about them.

A statistically trained student may not be impressed by the theorem notion that a random resolution to a tie is somehow undesirable or reprehensible, because repeating the random tie-breaker could produce a different result.

Elections do produce different results. That is the point of holding them periodicly. The point of theorems is to produce the same result, that is always true. Elections cease to be true even as they are held. They are snapshots of shifting popular opinion. It is neither here nor there, whether a different coin toss result changes the result. That is what happens, by the minute, with popular opinion anyway.

Objecting to an indeterminate tie break is what statisticians would characterise as "spurious accuracy."

I must admit I hadnt thought of the fact that a tie between two trailing candidates for exclusion is awkward, because subsequent elections of candidates could depend on a merely random choice of which candidate is excluded.

However, even this random effect can be redeemed to some extent. It would be possible to take three alternatives. Exclude either candidate or both. This leaves the chance of a majority decision as to subsequent possibilities.

Statisticly speaking, for a large number of candidates, a tie-break between candidates for exclusion is highly improbable. How often has it ever happened? Nobody knows, probably because it is that rare and insignificant an occurence.

For the sake of argument, let us admit the principle, that a tie for exclusion could randomly affect the outcome of elections to remaining seats. Let us even grant that it might conceivably change a seat between two evenly matched parties poised to implement diametically different policies.

Here I am actually loading the argument against myself, because I am piling a coincidence on a coincidence, that has nothing to do with the efficiency of the election system itself.
Never mind, what I am getting at is that "things fall apart."

The fundamental unreasonableness of the theorem critique is to apply deterministic standards to a statistical procedure. It is on the way to arguing that there is a logical possibility that the spilt milk could return to a re-assembled jug and the milk-maid uncry herself. This may be true in principle but in reality it is so improbable as to be no argument.

It is not even so much the applying of social choice theory on elections, where the harm comes in, as its subornment, or misuse as a false witness, against democratic election method. (We saw this clearly in the case of the Plant report.)

STV is held to breach the condition, Independence of Irrelevant Alternatives, thru Strategic Nomination (where “strategic,” in British speech, is “tactical”). This is less the spoiler effect in single-seat contests. Gaming STV, in general, rapidly becomes too much of a gamble with the increase in seats per constituency.

For example, Northern Ireland with STV uses a six-member system. In 2003, Sinn Fein in West Belfast hoped to gain an extra seat by a vote equalisation strategy getting their supporters to vote for their candidates in equal numbers, so their nationalist rivals, the Social Democratic and Labour Party, might be excluded first. And they would hope to gain transfers of next preferences from SDLP voters.

Instead, this vote management strategy led to the election of a Democratic Unionist Party candidate, the worst possible result for the strategists.

I might mention that the condition, Independence of Irrelevant Alternatives is akin to experimental use of a “control” of such masking factors.
STV controls, for voters unequal preferences for candidates, with votes transfered in proportion to a winners surplus. Whereas the spot vote counts unequal preferences equally.
STV also controls for unequal majorities, with a quota count. Whereas simple majority counts treat unequal majorities as equally representative.

It seems that the various attempts to game STV are kinds of tactical voting designed to influence the exclusion of candidates.

A method, Binomial STV, that I developed, does away with the exclusion count, to remove premature exclusion. This must also go a long way to remove theoreticly possible gaming strategies. Tho, they are unrealistic, anyway, mainly because the required preferential information is not available before the election to make their frauds possible.

Binomial STV brings out, more than ever, the nature of elections as statistical approximations, rather than deductive systems. Sometimes election results can be determined without doubt. In general, election method is a continuous search of the preferential information for the balance of evidence for the relatively successful candidates.

In principle, Binomial STV allows a systematic mining of the preferential data to go on indefinitely. Normally, the balance will settle fairly decisively in relatively early stages of counting or recounting.

Ill-chosen rules for judging election methods.

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A deterministic model of physics had to be modified by statistical interpretations. Likewise, a deductive model of elections is long over-due for an appreciation of the statistical realities of voting. In this respect, I refered, in passing, at necessary modifications to the conditions of Arrow theorem. Besides criticism in detail of this particular theorem, the whole approach of setting conditions or criteria for election systems has been counter-productive.

It made no sense to judge effective elections, only in terms of effective executives, effective legislatures, effective parties, whatever. You wouldn’t judge Euclid geometry a failure, because measuring the Earth, with territorial accuracy, did nothing to stop wars and deforestation in ancient Greece.

Other sets of criteria were closer to home, indeed tautological in the case of judging elections by the choice they give.

In promoting the Additional member System, the Institute for Public Policy Research even missed the criterion that elections are for electing. (It didnt get as far as The Goon Show finding that heat is hot: By gad, it's hot here. - It must be the heat!)

From failing the logical, even the tauto-logical, the first ippr criterion, of requiring a constituency link of voters to their representatives, illogicly requires elections to be locations. Constituency sizes may be adjusted by the levels of government that suit communities. Locations are no substitute for elections, as place-holders would have you believe.

The second criterion is "the system must establish a clearer relationship between the number of votes cast for a particular party and the number of seats it secures."

The article claims this statement will "ensure that principles of representation and proportion are embedded in a reformed electoral system."

Actually criterion two ensures not proportional representation but rather proportional partisanship.
Voting is for voters not for parties. This is something which the rule-makers keep forgetting.

As the ippr say, the reformed system must stop simply favoring the larger parties. They fail to add that it must also stop simply favoring parties at the expense of the rest of society to be proportionally represented.

Criterion three demands "all votes have a value" and the electoral battle should not be confined to a small number of marginal constituencies.

Criterion three is a consequence of criterion one, insisting on small constituencies. Merely adding Additional Members, leading to a reduced number of single members, does not stop parties concentrating their campaigns on the marginals. The reduced number of single members will create relatively more safe seats and yet fewer marginals to concentrate on.

"It is far from clear that the introduction of AMS has reduced the tendency for parties to concentrate in marginal seats. In part this may be because thanks to the relative paucity of list seats, parties can win a disproportionate share of seats by doing well in marginal constituencies."
(Changed Voting Changed Politics.)

Criterion four of "stable but not glacial government" echoes the Jenkins commission desire for a system that was not proportional enuf to always produce coalitions without periodic "decisive" one party governments.

This requirement confuses representation with social engineering. A truly representative election system will give the people what they want, whenever they want, not decide for them what it would be best for them to have.

The ippr report flies a kite for the minority dissent of Lord Alexander from the Jenkins report. It ignores the case for STV. Like the Jenkins report, it is prone to empty assertions, which are eminently contradictable. And sets a value on "continuity" (things must change so that things can stay the same).

Inconsistent rules for logical election method.

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Besides this and other cases of the classical method of deduction with irrelevant or ineffective axioms, in relation to election systems, there has been a failure to analyse voting methods themselves as axiomatic deductions. For the deductions to be logically true, the axioms of the deductive system must themselves be consistent.

For example, suppose the ballot paper of a referendum requiring a yes or no answer. If the voter answered both yes and no, the ballot paper would be disqualified, because it makes no sense. The voters truthful answer is either yes or no. He supports the issue or he does not support the issue. He cannot both support and reject the issue. Scotland cannot both leave and remain in the United Kingdom.

Yet the Mixed Member Proportional, alias the Additional Member System, commits to precisely that kind of inconsistency. One vote is for parties monopolising single-member constituencies. The other vote is for parties sharing multi-member constituencies.

Faced with a question, should we share or should we not share, if one answered, yes we should share and no we should not share, that would be a self-contradiction that tells you nothing, a paralysed decision.

That axiomatic self-contradiction, of AMS, proceeds to deduce a whole sequence of further self-contradictions in the construction of the system or rather anti-system. (I’ve discussed this, many times, and, in contrast, the consistency of STV as a theoretical system.)

Thus, the classical science of axiomatic deduction, applied to election methods, has widely resulted in irrelevant, poorly defined, illogical frame-works for the discomfiture of democracy.

A weakness of the axiomatic method is that it harks back to an "a priori" or before-the-fact conception of scientific procedure. Its first principles may seem inevitable. An experience of voting method suggests otherwise.

A widely accepted conception of the nature of measurement in the sciences, may offer a better basis for an assessment of election systems. (My earliest extant version, to be found on this site, is a paper in French for Unesco, in 1981. A later version, 1998, in English, is my two web pages on Scientific Method of Elections.)

Richard Lung.
15; 16; 17 May 2015.


Diane Ehr:- Voting Methods: Another Way to Choose.

Nicholas R. Miller: Monotonicity failure under STV and related voting systems.
(Uni, of Maryland.)

Michael Gallagher: Monotonicity and non-monotonicity at PR-STV elections. (Uni. of Dublin).

Oakley Benedict Gordon: Electing representative representatives. (Uni. of Utah).

Wikipedia: Issues affecting the single transferable vote.

Dr Phil McCarvill (Institute for Public Policy Research 2010): Devising an Electoral System for the 21st Century: The case for AMS.
[The title is justification by time-snobbery.]

Constitution Unit; School of Public Policy UCL: Changed Voting Changed Politics. Lessons of Britains experience of PR since 1997. Final report of the Independent Commission. (2003).

Geometric Voting and Consecutively Halved Positional Voting - Comparisons: Single Transferable Vote 2

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