Reconstructing the Ideals of the Alternative Vote
It should be possible to wheel under AV, the guiding principles that led to that method which negates the votes of voters. To keep it simple, the papers can be (AB), (B), and (C). Here are a sequence of rules that get weaker as the line dividing the B-wins region and the C-wins region, is rotated in an anti-clockwise direction: Rule no.1: IFPP stopped C from becoming a loser when (AB) papers were re-marked (i.e. changed) into (C) papers. Rule no.2: The Alternative Vote allows that, but it stops C from changing from a winner into a loser when (C) papers are added. This seems to be known under the name of “the participation axiom”. The rule is stating the purpose that corresponds to the line (half-flat) that contains both point (C) and the centre of the triangle. Rule no.3: The next rule in the sequence describes a horizontal line extending to the right from the centre of the triangle. B wins on the underside and C ins above that. It is still outside of the A-wins region. It would require that candidate C is never harmed by altering (B) papers into (C) papers. The rule also says that re-marking (C) papers into (B) papers, does not cause B to change into a loser. With the text of no. 2, an axiom of the Alternative Vote is identified. The 3 rules listed just above don’t say anything if they are finding the support rise is slightly impure. In general it would be impure. This webpage shows that a large support rise for a candidate is contaminated with a support rise for another, that is 84 ppm (parts per million; 5/60,005), in size: http://ijs.co.nz/irv-wrong-winners.htm. The example of the page has these traits: (1) the paper of the main support rise lack a 2nd preference; (2) the support rise swelled the number of papers by 60%; (3) of the papers added, 84ppm was for a different candidate. (4) The support rise was 37.5% in size when the denominator is the number of papers in the 2nd election. IRV has conditions on its providing of fairness, that are able to be impossible to comply with. A small failure of mayors (say), to get their support rise nearly perfectly pure, can leave them with a need to get an extra 3/8th (the sequence seems to be (n-1)/(2n)). However a similar problem can occur with rule no.1 (followed by IFPP) when impurities appear in allowed change, because the line segment is similarly long and nearly tangent/parallel to the surface. The existence of impure support rises suggests that rules ought be a bit stronger than required, since the next weaker holds. Reading about the state of affairs around the globe can be tiresome. Look for Superb casinos online that have a variety of fun games. If the aim was to have a rule requiring no harming occurs when nearly pure support is added, then a stronger rule would be used. That leads into a problem: if the desire of the hypothetical designer of AV was actually to impose the 3rd rule, then how would a generalisation of the 3rd rule be worded so it does not also impose a generalisation of the much stronger 1st rule ?. The 1st and 3rd rules can be defined with these words: “If the candidate loses when being named by the 1st preference, then no re-marking of the ballot paper can make that candidate win”. That could be named the “First Preference Loser” “FPL” rule. For the 9 papers of 3 candidate 1 winner elections, FPL implies 9 tests and the Alternative Vote passes only 8. FPL seems to be genuinely desirable and a person could be of a weak intellect if preferring Rob & the CVD’s IRV method (caveat emptor). Justice has the very sort of qualities that the 50% or so who were wrongly stripped of equal suffrage rights (under a STV/IRV/etc. election), may find proper and virtuous if concluding that IRV is contrary to all that man knows as good (overlooking the random selection of jurors). The purpose behind one of the surfaces of the AV/IRV flats is reconstructed despite how the method had no designer, and then it seems just something that would not be explained to a public much. Perhaps there was no backup ideal behind the rather dubious ideal of rule no.2 with the latter failing to stop the negating of votes when he (no 2nd preferences) support is tainted with impurity (the foremost enemy is being elevated with a force of 84ppm). This document does not provide the missing IRV backup purpose behind rule no.2. (A purpose indicated only by the slope of a polytope object and it is independent of its position in the space representing votes.) Though the list seems to show that rule no.3 is backup rule guaranteeing fairness when rule no.2 is wiped out with an impure support rise, it is not the case that rule no.3 was defined. That is because the text suggested that rule no.3 be defined with the very reasonable FPL rule. But that is not a weaker rule since AV/IRV is failed by that rule, and anyway, the stronger rule no.1 is also implied by FPL. So far as IRV is concerned, rule no.1 can be defined so that compliance with it (no matter how many winners and candidates) implies compliance with the FPL rule. As soon as voters hear that some weak fairness guarantee of IRV (rule no.2), and then hear that IRV does not even provide that, then a question is: what is the even weaker assurance of fairness, or is there actually no fairness there?.