Perhaps the strongest charge against STV is the fact that a candidate can sometimes get more votes and do worse, all other things being equal.
The problem of non-monotonicity (monotinicity failure) is not as simple as presented in the above description (although that is the usual way the situation is presented).
Nor is it common.
Nor can it be manipulated by a voter.
So is not really much of problem at all.
A candidate cannot get more votes and do worse unless another candidate's vote tally changes and even than not always does the candidate do worse.
Most presentation of monotonicity failure say that that kind of failure occurs when a candidate gets more votes and does worse, all else being equal.
But for a candidate to get more votes and for all else to remain equal is actually impossible --- if a candidate gets more votes, then either the total number of votes must increase or another candidate must do worse. And it is the worsening of the other candidate that actually causes the monotinicity failure, when it does happen.
A candidate can never do worse by getting more votes. But another candidate doing better or worse may help or hurt another candidate, due to the way that vote transfers arising from elimination of candidates works.
say we want A to be elected;
votes for candidate E each carries a next usable back-up preference for A;
votes for candidate D each carries a next usable back-up preference for B.
D is second from bottom of candidates by popularity, and E is the least popular.
the votes for E carry a back-up preference in favour of A, so if E is eliminated, A will get more votes.
But if D's vote tally drops, D will be eliminated and his vote transferred, not E's. (at least E's will not be transferred immediately).
But sometimes back-up preference are not used, or do not benefit A -
if D is never eliminated despite the drop in votes, then those back-up preferences marked for B are never consulted.
if D is eliminated at the end, and the seats are thereby filled or set to be filled, then the votes are not transferred to B.
If A is eliminated before E, then A does not get votes from E.
If E is elected, only some of E's votes are transferred, or all of E votes are but at fractional value, so A will not get full benefit from E votes' back-up preferences.
Non-monotonicity is based on idea that a drop in D's votes is produced by a rise in A's votes. and therefore a rise in A's votes means D, not E, is elminated. and therefore the next vote transfer helps B, not A.
That may be true for the next vote trafer but may or may not have any effect on the end outcome. If E and A make up a quota, and E's back-up preferences are for A, likely the lesser of the two - E - will eventually be eliminated and A will be elected, no matter the distribution of the votes between them.
monotonicity failure thus is produced only under special circumstances:
Monotinicity failure does not occur in these circumstances:
if A's votes rise enough to pass quota, he is declared elected - no failure, even if E's vote tally drops.
if A's votes rise enough to stop being the least-popular candidate, at a time when the least-popular candidate is to be eliminated, then no failure, A stays in game where otherwise would be eliminated.
same for if A wins the tie after a rise in A's votes puts A tied for least-popular candidate at a time when the least-popular candidate is to be eliminated.
if a rise in A's votes help it stay in game and it wins a seat at the end without quota, then no failure.
if rise in A's votes are at expense of D and D is never eliminated, then no failure.
if a rise in A's votes are at expense of E, and E is eliminated and E's back-up preferences make votes go to A, then no failure.
Only if rise in A's votes does not make him or her pass quota immediately, and comes at expense of D who is eliminated and D's vote transfers do not go to A (but to B as prescribed in the model), then failure.
Like I say, only in very special case.
The fear of monotinicity failure apparently is that A's votes rise, at expense of D, whose back-up preferences are not for A. D is eliminated, helping B get elected, while A's backp-up friend E is never eliminated so A never gets help from E's votes.
This cannot happen in STV contests where seats are filled at the end by partial quotas (such as optional-preferential voting).
In such STV contests, the result for A and D is either elimination or election.
(There are no candidates who are neither elected nor eliminated.)
If A is eliminated before E, E's back-up preferences cannot help A.
(A's back-up preference may or may not help E, just depends how voters marked their preferences.)
If E is eliminated before A, then his back-up preferences will dictate that the votes go to A.
If A starts out more popular than E, and all or most of D's votes are marked with back-up preferences for A, and E is elimanated some time in the process, it mostly does not matter whether E is eliminated early or late. Either way eventually A receives those votes and if A and E together have a quota, then A will be elected.
(In fact if A gets more votes and it is at expence of E, then it is more likely A will be elected because E will be elminated sooner rather than at the end when his votes may not be transferred. so another counter-argument to the idea that more votes means less chance of success.)
Only if E is the last candidate to be eliminated, and his elimination thins the field of candidates to the number of remaining open seats, then A does not get benefit of E's back-up preferences.
and then it is up to A by himself or herself whether or not his/her vote tally is enough to beat out others to win a seat by plurality at the end. And in that case having more votes (the source of the purported monotonicity failure) is a help, not a hindrance.
If a voter cannot presume that a special case where monotinicity failure will apply will happen, then there is no way to know that helping a candidate may hurt him, that switching a preference may be best way to get intended goal, because in most cases it will not work that way.
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Aaron Hanner in his thesis
Single Transferable Voting - Features of Democracy and a Comparison of STV to Alternate Electoral Systems
(B.A. thesis, University of Virginia, 2016
(available online))
addresses the matter at some length, giving flesh to my brief essay above.
He modulates the situation by saying that candidate A gets higher rankings, thereby implying that another candidate gets lower ranking. This is clearer way than simply saying candidate A getting more votes does not.
It clearly shows "all other things being equal" just does not apply.
Non-Monotonicity and Monotonic Failure.
A voting system is defined as monotonic when a candidate cannot be harmed by receiving additional votes (or in ranked-voting systems, being ranked more highly), or vice versa, all else equal. [most presentations of non-monotonicity do not say all else equal but merely imply or assume it to be a given. And in fact most break that rule, either another candidate must get fewer votes or the total number of votes must be increased - "all other things" do not remain equal.]
If a system does not meet this condition, it is called non-monotonic. Put another way, non-monotonicity occurs when it is possible to make a winning candidate lose by ranking them higher or to make a losing candidate win by ranking them lower.
(Forward monotonic failure (FMF) occurs when a candidate is defeated due to higher ranking (more votes),
and backward monotonic failure (BMF) occurs when a candidate wins despite higher ranking (fewer votes).
Simply because a possibility exists does not mean it will be realized, however. When non-monotonic properties actually manifest themselves, then it is called monotonic failure. A prominent study by Gideon Doron and Richard Kronick73 demonstrated that STV is non-monotonic, a discovery later elaborated upon by Steven Brams and Peter Fishburn.74
The controversy over monotonicity is currently the most active site of debate regarding
STV’s adoption. Not only do many FPP advocates consider non-monotonicity to be STV’s fatal flaw, it is also the lynchpin of Michael Dummett’s argument against STV in favor of the Borda count, which is monotonic.
However, determining the true impact of non-monotonicity is extremely difficult. The greatest roadblock is that monotonic failure by definition is a counterfactual.75 Seeing how voters did vote is relatively easy – one simply needs to obtain the full set of ballots. Proving monotonic failure, however, requires knowing how many voters might have voted a certain way under different circumstances, all else equal. Given the sheer number of permutations possible on an STV ballot and how any change may have extensive ripple effects, this prospect is virtually hopeless. Real-world data on STV elections is relatively scarce, as we have mentioned, and building realistic models to draw conclusions is easier said than done.
Unless a real-life STV election must change its outcome as a result of discovering an error where rankings were incorrectly recorded on certain ballots, it is practically impossible to definitively prove monotonic failure. These factors present serious challenges for both advocates and opponents of STV to make comprehensive arguments, but the evidence we do have suggests that STV’s non-monotonicity may not be as disastrous as supposed.
First, Doron and Kronick’s landmark model proving STV’s non-monotonicity is quite contrived. While the model technically uses STV, its electoral design is atrocious. The district has only two seats, while at least five is generally considered to provide optimal proportionality.
There are only four candidates, twenty-six voters, and five unique ballot profiles (four in the D’ example demonstrating monotonic failure). Although one could reasonably predict certain ranking trends based on ideological patterns, such a lack of diversity in ballot profiles seems misleading. The Brams and Fishburn examples are similarly contrived, using poor electoral design and a small sample size. The studies achieve their purpose of showing that STV has non-monotonic qualities, but do little to suggest that monotonic failure would occur under real-world conditions.
Second, both of these examples and in fact most discussions of STV’s non-monotonicity
(even by STV advocates), tend to treat candidates in a vacuum, with no regard to their placement on a political axis. For example, using the ‘real’ election D in Doron and Kronick’s model (as opposed to D’, which demonstrates monotonic failure), candidate proximity scores for the four candidates W, X, Y, and Z can be calculated. These scores show how many voters ranked two given candidates directly adjacent to one another. Results are shown in Figure 2.
For example, the top row indicates that four voters ranked W directly before or after X, five ranked W directly before or after Y, and seventeen ranked W before or after Z.
... [explanation not copied]
Michael Dummett also accuses STV of being “quasi-chaotic” and electing officials [members] “virtually [at] random” because monotonic failure occurs under STV as a result of the order in which candidates are eliminated.
But if monotonic failure likely affects only spatially adjacent candidates, it is not random, and in fact is quite systematic. Dummett treats candidates in a vacuum rather than interrelated points on a political axis. Monotonic failure is certainly not ideal, but also not nearly as disastrous as STV opponents suggest.
If there were to be an incident of monotonic failure under STV, it seems most likely to only affect spatially adjacent candidates, resulting in tolerable differences in outcome.
The most pressing question, of course, is how often we might expect monotonic failure to actually occur under STV. Possibility in theory does not necessarily mean likelihood in practice.
Answering this question has proved difficult, however. When Doron and Kronick proved STV was subject to monotonic failure, most STV advocates simply dismissed it as a remote possibility and unlikely to affect an actual election, but this was based on intuition rather than data.
The most concerted effort to establish a real answer has been by Nicholas Miller, who in a 2002 drafted but unpublished paper was able to develop graphical models using triangles (representing three-candidate races) and depict the ‘spaces’ inside them where monotonic failure would actually occur.80 While the models were somewhat workable, Miller hit a dead end in using them to arrive at a definitive conclusion.
Since then, most research involving monotonicity failure has been done on three-candidate IRV rather than STV, but since both systems use the same elimination mechanism, some useful insights may still be extracted.
There are two types of monotonic failure.
Forward monotonic failure (FMF) occurs when a candidate is defeated due to higher ranking,
and backward monotonic failure (BMF) occurs when a candidate is victorious due to lower ranking. Perverse incentives are stronger to manipulate BMF than FMF [I don't know what this means]; one may actually increase a preferred candidate’s chance at election by ranking them lower. [he just said this so don't know what he meant by repeating it - perhaps he meant - and does say later - trying to win by lowering votes is not likely to succeed and perverse, while giving more votes to a preferred candiate is true to hope and then disappointingly dashed by the meachanics of STV - sometimes.
BMF is both improbable and risky to try and manipulate under the elimination mechanism used by both IRV and STV, wherein the least-popular candidate is [successively] eliminated.83
It is estimated that 5.74% of three-candidate IRV elections have conditions where either type of monotonic failure may occur, with an actual predicted incidence of at least 1.97%.84 Vulnerability to monotonic failure also increases with the size of the electorate.85 [this statement is counter to expectation and logic -- when thousands of votes are valid, the change of one vote is not likely to change the outcome.]
Conditions differ between STV and IRV, however.
STV tends to have larger districts and thus electorates, but also more candidates running since districts have multiple seats. How these factors may effect monotonic failure under STV compared to IRV is difficult to determine, especially since no STV election is the same. The number of voters, seats, candidates, and relative popularity between candidates may vary wildly between districts and elections. Each of these factors has a direct impact on whether or not monotonic failure occurs.
It would also be practically impossible for voters to strategically exploit monotonic failure.86 While one or more voters could theoretically engineer a monotonic failure to their advantage, the actual likelihood would be negligible, especially as the number of voters needed increased. [two votes are not likely to make a difference] As we have discussed, ballot strategizing under STV is virtually futile.
If monotonic failure actually were to occur, it would almost certainly be the result of chance. Most likely, indecisive voters would rank one candidate slightly higher or lower than another who they preferred to a similar degree. Given these conditions, both candidates would most likely be adjacent to one another on a spatial model. Monotonic failure would therefore have a minimal effect on the Chamber’s representativeness, and thus not violate the demos criterion. [Hanner here is assuming that the one who gets more votes and is denied a seat is close in belief to the candidate who is now eliminated, which is not ture - the one who is now eliminated does not -- does not -- give most of its votes to the first candiate. if it did, there would be not be the failure.]
Brams and Fishburn argue that STV’s non-monotonicity violates a “fundamental democratic ethic.”87 This thesis argues, however, that the fundamental democratic ethic is in fact the demos criterion – to represent the people as accurately as possible.
Non-monotonicity is certainly not an ideal feature in a voting system, but it does not violate the demos criterion.
Monotonic failure is a mathematical peculiarity arising from the computational mechanism STV uses to determine winners. It cannot realistically be manipulated or exploited, and is virtually impossible to detect due to its counterfactual nature.
It is possible but unlikely to occur, and if it does occur, unlikely to have a meaningful effect on the representativeness of the Chamber itself.
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An essay by McCune in US about the math of STV:
tries to point out how STV is flawed
But I think the charges lack power.
For one thing he uses worst-case scenarios of single-winner IRV to show inefficiency of STV.
Here is conclusion of the essay - but the evidence does not convince me.
"5.Conclusion
Mathematically speaking, STV can be a funny voting method. As we have shown, the method can behave in pretty wild ways when we enlarge the electorate. More broadly, STV can also produce paradoxical outcomes when we remove ballots (producing no-show paradoxes) or when we shift candidates up or down the rankings of ballots (producing monotonicity paradoxes). Such strange outcomes point to a core of mathematical wackiness in the design of STV. Many of the examples in this article also illustrate STV’s instability, in the sense that we can perturb the ballot data in relatively minor ways and produce large and paradoxical changes to the winner set in response. Whether the reader finds these issues problematic or not depends on their values and approach to evaluating electoral procedures; at the very least, STV allows for some mathematical fun that other (perhaps more reasonable) methods do not."
But looking at the essay from the top, we see it opens with less-than-convincing sleight of hand.
The essay begins by presenting this apparent paradox
"You ask your campaign manager, “Is there any way I could have won?” and the manager responds, “You could have won if the turnout of voters who dislike you were increased.”"
Not stated is that this outcome is based on "increase in the turnout of voters who dislike you" means a decrease in your own votes (so it is not true to say everything else remaining equal)
and by your own votes, it means the votes that go to your party, not to you personally. specifically the amount of votes that a lesser candidate of the same party receives, is less. It is assumed that the votes belonging to the lesser candidate will go to "you" if transferred. But STV makes no such assumption.
with fewer votes,
the lesser candidate may be eliminated too early and thus the party not have enough standing candidates to take all the seats it is due, if we are looking at party-wise results
or the lesser candidate might be moved into a situation where his votes cannot assist 'you" in being elected.
This happens if the lesser candidate is
A. neither elected nor eliminated, or
B. is being eliminated too late for his votes to be transferred. (often this takes form of candidate being declared defeated after last count)
thus his vote transfers not assist "you".
Situation A cannot happen in an STV election where there are at least some exhausted votes - any STV contest where members are elected with less than quota means there are no candidates who are neither elected nor eliminated.
which means Situation A not applies to contests held where voter decides how many preferences to mark.
(As well, a lesser candidate can be put into situation A or Situation B either by receiving more votes or by receiving fewer votes, or might have been in Situation A or Situation B anyway in the election and still "you" were not elected.
And the winners who did win might have won despite the lesser candidate of their party being in Situation A or Situation B, so it does not necessarly mean bad news.)
It is sort of same as saying if "you" had held your tongue differently or worn different colour socks, "you" would have won. Maybe you would have, and maybe not.
Lucky breaks in distribution of party votes likely impact all parties equally in the long run, and anyways they have much less impact than under FPTP.
I have not read more than that in the article but I would be surprised if the rest of article is not the same -
-hidden connections that hide why what is presented as a ludicrous situation actually has basis in good mechanics (more on that below)
-presenting obscure possible cases as true and common problems.
-concealing how STV's use of MMD means all substantial parties do get rep. even if some individual candidates are not elected who with lucky breaks and expected concentration of party votes behind them would have.
Like under any system, under STV a candidate who gets more votes is always more likely to be elected than one with fewer.
The sort of problem presented there (perhaps article gets more nuanced later, I don't know) is part and parcel of mechanics of STV -
if we took first-preference votes and allocate seats to parties based on that, we would ensure that no party would suffer from bad candidate eliminations and would benefit from party votes being lumped together behind party's electable candidates.
But STV does not use parties in vote count.
it looks at votes cast for candidates.
Such care opens door to votes crossing party lines, which is hailed as promoting cross-party co-operation.
All PR systems produce minority government (almost always) and thus promote cross-party co-operation
but as well in STV, cross-party support (based on individual candidates) or at least evidence of ranked party support /back-up party preference, is seen and demonstrated even as voter casts votes (marks preferences).
some might say voter showing preference for more than one party takes away from party prop.,
and that final seat allocation P not conforming to first-preference-vote P takes away from party prop.
but those are elemental components of STV, put there for the reason that votes can cross party lines if voter desires and situation requires or allows it.
votes first cast for cand of small party or less-popular cand of large parties are shifted, sometimes across party lines.
In STV about half the votes are never transferred, other than as surplus votes of winners,
and in the end 80 to 90 percent of votes are used to elect someone preferred by voter over others.
there are obscure examples where due to bad candidate eliminations, or too-small candidate slates (such as SNP's unfortunate under-rep in last Scottish election),
dis-P outcomes are produced
- a party or two suffering under-rep., (under-rep. but not total lack of rep)
- a candidate saying if the breaks had been different, if all his party's votes had come to him, he could have won, therefore he should have won, therefore the system sucks.
but the overall effect of STV is fair and most votes are used to elect someone, (even that means outcome is diff from first preferences and is different from outcome under party list PR and MMP)
the trade-offs are:
vote being able to cross party lines (meaning less waste) versus vote not being allowed to cross party lines (more waste in cases where electoral threshold in use, or where ever the effective threshold bites)
cand voting versus party voting
ranked voting/transferable votes (less wasted votes; less strategic voting) versus X voting/no vote transfers (more wasted votes; more strategic voting).
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STV are the choices on the left (before the "versus")
party list PR are the choices on the right
MMP has two levels
district level:
vote not being allowed to cross party lines
cand voting
X voting/no vote transfers (more wasted votes)
top-up level:
vote not being allowed to cross party lines
party voting
X voting/no vote transfers (more wasted votes, at least more than if votes could cross party lines)
every system has advantages and disadvantages (potential accidental outcomes).
or at least present applications of any system have produced accidental outcomes.
But all PR systems are better than FPTP or Block voting.
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