I did not find much of value in Arrow's Impossibility theorem as i outline in discussion of online video online.
esp Arrow's unanimity rule - in real life elections never do all voters vote unanimously.
and no one has pointed out where or if i erred.
(see below for more discussion of Arrow's Impossibility theorem)
RANKED VOTING
Someone might say ranked voting or Instant-runoff voting is only one dimensional, that neither of them can handle sets of choices that fit on more than one dimension.
But voting is always a yes or no deal.
Ranked voting as in STV and IRV (echh) is yes or no, but with backup options that come into play under certain circumstances
voter says i vote for A but if vote cannot be used for A, then move it to B.
But as Scottish PR expert James Gilmore has pointed out, an election in a MMD usually means a party runs more than one candidate.
thus you can vote in more than one dimension:
-a woman and a Democrat (U.S.) (Liberal in Canada) just as an example
or
-both for a Conservative and guns right advocate to use a stereotype as an example.
or
-for a candidate from your town if you are in a spread out riding who also ascribes to your view of global warming.
for your first preference you can choose the combo that best fits your mash of priorities.
then for your second choice you run along the biggest priority of choosing some one of same party, or same view of gun control or global warming , or micro-local allegiance or gender, or other, etc.
then when you run out of options along say the party list, you return to second priority line say view of global warming or carbon tax, and go to second-preferred gender for example to carry that line.
and so on
But those are just ideas - the votes has compete liberty to mark his or her backup preferences just he or she wants.
or in the best systems (IMO), not to mark backup preferences at all if there is only one Green party plumber and that viewpoint is only viewpoint that voter cares about.
the single voting is a valuable limitation (as oxymoronic as tht sounds)
you cannot vote for a mix, but at same time single voting in a MMD means no one group can take all the seats.
PR means separate groups are formed and each group gets its due share of sets in district.
single voting in MMD is in line with this.
under STV (and IRV (eghh) you cannot vote for mix but you can vote for a single candidate who is fiscally conservative and socially liberal so can vote for a mix that way.
while under FPTP if you want fiscal conservative, you vote for say Conservative party candidate, no mater what his stand on social issues (because there is only one Conservative (U.S. readers read Republican) candidate
or if you are socially progressive you vote not for Conservative but vote for the one Liberal or the one cand of other non-C party and open yourself up to tax and spend policies (U.S .readers read Democrats)
(all of course based on stereotypes)
Under STV, if you don't give your first pref for your preference, you are working against your interest.
If you give your first pref for L and that candidate is not elected or eliminated, your vote will not move. Your backup pref will not be even consulted so it is not at all important how you mark your back-up preferences.
in fact, if you give your first pref to C, hoping to get votes transferred to A so A wins, you actually did the wrong thing because C having more votes may mean its back-up pref. (the route by which vote would go to A) are never even looked at because C will not be eliminated.
STV's logical trap is sometimes presented that if you give your first pref to A, it means C gets fewer and and is eliminated and C's backup pref. come into play and that means C's votes are transferred and they go to B, or go to B at high enough rate compared to transfers to A, that B surpasses A, so B wins.
But that is how it should go anyway -- more voters preferred B than preferred A so it is just, even if A voter dislikes outcome.
Where voter not required to mark most of the candidates, there are enough exhausted votes that all candidates are either elected or eliminated so there are no candidates neither elected nor eliminated
so all votes are either exhausted or marked for winners
except for votes belonging to last-eliminated candidate in some cases, whose votes are not transferred (but by definition they are less than one quota).
likely perception of where ranked votes don't seem to work is people reading too much into back-up preferences.
the candidate with the most votes wins
and anyways if it is IRV (egghh), how much election justice did you expect?
if people try to manipulate ranked voting, they often get egg on face.
Give your top (lower-number) prefs to your preferred choice , and you likely not suffer at all,
but more often, you will suffer if you mark your vote first for people you don't really want to see elected.
In last Northern Ireland election, in some cases Sinn Fein ran just one candidate (East Belfast, East Antrim etc.) so no need to get fancy,
just simply appeal for first preferences to the one SF cand. was their best strategy.
but perhaps elsewhere they did get fancy and perhaps got more than they might have in worst case,
but in the end, Sinn Fein got its about perfectly due share of seats -
- with 29 percent of vote, SF got 27 seats in 90-seat chamber.
Two strategies are sometimes tried to game STV:
-spread out votes across party list so candidates not eliminated
-concentrate party vote on one and then benefit from cascade
oddly the two are totally different.
===
In conclusion,
single voting in MMD produces mixed rep in each district
ranked voting in STV produces even higher proportion of effective votes and even better PR of parties in the district.
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ARROW's IMPOSSIBILITY Theorem
video by "Veratsium" on Arrow's Impossibility
Either he mis-presents it or Arrow's theorem does not hold water, IMO
the maker of the video says democracy is impossible
but obviously only envisons elections electing single winner
and nowhere makes mention of how many votes are used to elect the winner,
fully low in or un-necessarily high in FPTP;
about half in IRV, usually
about 80 to 90 percent in STV.
not anything about PR
sequence of the talk produced by "Veratsium"
- failure of FPTP to elect majority choice in the district hence false-majority government (somewhat conflating district results and make-up of chamber)
- endorsement of IRV
-but saying IRV is flawed by fact that if a candidate gets fewer votes, it can do better.
this may occur but only when -
-candidate A gets fewer votes, another candidate gets more. so not case where all other things stay the same.
-When Candidate A gets fewer votes and Candidate B gets more, Candidate C is eliminated and gives votes to Candidate A, not to Candidate B.
so that weakness only applies in exceptional cases and is not case of all other things staying the same
Conversely IRV is flawed because candidate getting more votes may mean he/she is not elected, because of how it affects other candidates' vote tallies.
or when Candidate gets more votes or when candidate A gets fewer votes, it may have no effect at all on whether or not Candidate A is elected.
describes how this purported failure was addressed by Borda then by Condorcet...
says Condorcet one-on-one vote comparison method was invented by Lull in about 1300s! but then lost and only rediscovered in 2001.
Tarski, Lewis Carrol mentioned but only in passing
then at 12:26 yes Arrow's stuff (see below for my critique of Arrow's ideas)
by 15:31 he is talking about how society ranks candidates based on preferential votes.
so not necesarly choosing a winenr but determining "society's rankings."
[i'm barely hanging on as it is not concerning how to elect in most efficient way possible,
nor about PR as far as I can see but only single-winner or not even about filling a seat at all but playing with how to measure general sentiment.
plus he shows voters marking their ballot with a tie for A and B.
Interesting if you lilke that sort of thing but as far as I can see, not useful in real elections where you can't mark ties.
at 18:00 he has talked himself into situation where C has five first choice votes, A only one, but A is "ranked" by "society" as more popular than C.
[not enjoying this...]
It seems, according to him, that if five vote A and five vote B, but one switches from A to B, then B wins due to this "pivotal" voter who he calls a "complete dictator."
yes, 1 vote may have an impact but hardly ever does,
and anyways that power is held by any one of the voters who voted for A,
in certain cases under any system, there is a tipping point where one candidate goes from minority to majority or from losing position to winning position, so what?
"where three candidates, no way to rationally aggregate voters' preferences -- you always need to give something up."
yes, if you only have one winner.
he is not talking about multi-winner PR
he is not just taking X votes and seeing who are the most-popular based on first choices and electing them...
is he trying for largest proportion of effective votes?
seems not -- he is trying to determine "society's ranking", whatever that is.
talks of Black's median voter idea -- median voter will be pivotal voter and thus apparently fine to be "dictator"
19:50 he says Arrow's impossibility theorum applies only to ranked votes (leaving out X voting altogether)
and then says Arrow's impossibility theorum does not apply if votes are rated.
ignoring that ranked votes as used in STV are not ranked votes in the way that he means ranked votes
now he is saying Rated votes by which he means differently-weighted ranked votes.
in his examination earlier, he was using a vote marked A, B C to give higher ranking to A. so actually he was weighing it before, he just did not make any mention of how first choice was weighed higher than lower pref. but it was.
19:59 approval voting
photo of voters shows at least one voter previously quoted as saying they prefer only one person,
perhaps all of the photos are recycled like that.
it was never previously mentioned that the voter in one of the photos expressed having any problem with X voting.
likely true for other photos shown
he simply took photos of voter voting with X votes (India) and presented them as voting approval voting.
[his (their?) vote might have been ignored under FPTP but he (they?) expressed no problem with X voting.
in fact under any system, not all votes are guaranteed to be used to elect a winner, esp. if there is only one winner. ]
(nowhere in his aggregated preferences talk, does he say how many voters see their first choice elected.]
20:37 shows he is definitely only talking about single-winner
21:13 he asks if it is true that democracy is mathematically impossible?
yes, he answers if ranked voting is used, "which most countries use to elect their leaders"
I doubt that most countries in the world use IRV or any form of ranked votes, to elect their leader.
I would guess most countries instead use
Electoral college (U.S. and others),
X voting (likely many places)
or
do not directly elect their leader at all (British-style parliaments, including Canada and UK).
Ranked voting is meant to provide solution, not create more problems.
ranked voting provides deeper info than X voting, and higher proportion of effective votes.
if it simply creates problems, then use X voting.
but get away from Single-winner contests anyway!
he wraps up by saying (paraphrased)
"some methods are better at aggregating people's preferences than others, [whatever that means]
FPTP is particularly flawed [although it is not ranked voting at all.]
But that does not mean we should not try to find most perfect system."
l hope he discovers benefits of multi-winner contests and PR -- and soon!
================================================
I agree there are certainly unstated conditions under which democracy is mathematicall impossible,
for one "democracy" as he sees it has to accomplish five things put forward by Arrow in 1951
they are at least clearly explained starting at 12:27 and listed at 14:04 .
it might be a weekend - or a lifetime's - work to take his five "conditions" and show how fair voting in a MMD achieves them,
thus dispelling how "democracy" (representative democracy) is impossible.
(But most of Arrow's concerns are not shared by me or even apply in real-life elections, IMO:)
1. unanimity which is either impossible in real life as per first choices (or is possible if you say that because all voters rank all candidates and one of those candidates is elected that means the voters are happy, which I take it is how rated voting works. (said somewhat tongue in cheek)
2. "no dictators" i think he means majority rule
3. "unrestricted domain" (at 13:20)
i see it as combo of
- no random-ness (althogh that does not mean that there are not rules that thus say one result when diff. rules might produce diff. results
example: Gregory, IGM, WIGM might produce diff results compared to each other but each has no randomness.
-no votes can be ignored, all must be used to elect winner (surely an impossible condition. perhaps I did not hear right.)
4. "transitivity" (at 13:40)
apparently saying if each voter is same and prefers A over B and B over C it must prefer A over C.
why this is important in single winner contest I have no idea or even why it is important in any election, I have no idea.
A is sure to win by unanimous approval.
and anyways voters are not all alike.
5. Independence of irrelevant alternatives
if people prefer pizza over sushi, then a burger store opening next door should not affect what people eat, or something like that.
I don't see how Arrow's high valuations of people's secondary preferences are important.
but I admit others might...
STV does not consider secondary preferences unless ballot would be wasted otherwise.
list PR does not even have voters mark rankings (usually)
SNTV does not even have voters mark rankings
looking at secondary preferences and using them potentially against voter's first choice is actually why Buckley form of STV was found to become simply SNTV, (in Cleveland in 1920s) because voters could not trust in the power of their first choice if they marked secondary preferences.
maybe instead of taking Arrow's five conditions and trying to apply them to PR,
we should make up five (or more) conditions that we think a reasonable and rational election system should have.
1. majority rule is obvious. corollary: A minority should not take majority of seats.
2. right of minority to due share of seats (not mentioned by Arrow)
a voter's secondary preference should never be used against his or her first choice.
No voter should be hurt by marking secondary preferences.
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the approval voting the presenter envisioned involved using ordinal voting from -10 to +10. but allowing breaks between numbers - is that cardinal voting?
some ranked voting actually uses X voting -- you put an X in first-preference column, an X in second-preference column. etc.
but in Ottawa MMD, without ranked votes, it is not likely that one-seventh of vote would take one seat in 7-seat Ottawa district as general rule.
nice idea but actually many votes would be wasted, likely about same portion as under FPTP.
but more fairness as members of diverse parties would be elected in the district, just not with any set number of votes.
more people would see someone elected in district they at least partially agree with.
Ottawa MMD behaviour would be like MMDs used in Vanuatu elections where SNTV is used. it is easy to see members there elected with 5-10 percent of the vote even where seven members are elected.
but then we start to use ranked votes (STV), then you can have quota and scientific levelling out of candidate's vote tallies.
but not with X voting (or cardinal voting).
SNTV might be good as first step toward fairness in Canada.
it would be an advance over FPTP.
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Arrow's theorem seems single-winner and pent up with reference to secondary preferences so not PR at all.
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