This is a Reply, by us, to the op-ed
"How Majority Rule Might Have Stopped Donald Trump"
By Eric Maskin & Amartya Sen,
New York Times, Thursday 28 April 2016.
We will correct various errors and omissions therein, provide facts refuting and/or supporting
M&S's claims, and provide a simpler and we think better proposal and about 20 reasons
to prefer it over M&S's. (See also short
"letter to editor," rejected by NY Times.)
Maskin & Sen complain that
the 2016 USA Republican Presidential
Primary is currently led by Donald Trump.
That is despite his
28.4% approve, 65.4% disapprove
rating nationwide from 19 March to 26 April, which will make
Trump by far the most-disapproved major party presidential nominee in
US history during the polling era.
Fact check #1:
M&S insinuated (without giving supporting data) that Trump would
have lost many state one-on-one races to some of his rivals:
Maskin & Sen: "...[Trump] could well have been defeated in most states
(given his extreme views on many subjects) had the opposition
coalesced around one of his leading rivals."
Since there is actual poll data on this topic, we can check this claim –
and we find state poll data fails to justify it.
Specifically, of the 9 states with primaries held before
M&S's op-ed for which I found pairwise poll data,
Trump officially won 8 of them, and still would have
won 6 using those states' "majority winners"
based on their pairwise polls (the winner would have
switched Trump→Rubio in NH and NC).
Also, Trump won over 50% of the vote in each of these 17 states
AL, AZ, CT, DE, FL,
GA, HI, IN, MD, MA,
MO, MS, NY, PA, RI,
out of the first 40 state primaries.
On the other hand, M&S's claim would be well-supported by
nationwide pairwise polls of GOP primary voters –
all those I could find indicated Rubio would
have defeated Trump pairwise.
Cruz also would have defeated Trump
based on averaging 5 pro-Cruz polls with 1 pro-Trump poll
to resolve their disagreement. (But Trump would have
defeated Kasich pairwise,
based on averaging 2 pro-Trump with 1 pro-Kasich poll.)
Pairwise polls & GOP 2016 primary results. In chronological order
by date of primary (or national poll).
(Also 54% of US would "definitely not vote" for Trump in general election,
regardless of opponent).
Fact check #2:
Maskin & Sen also insinuated
that in the 2000 US presidential election Al Gore would have
been "majority winner" in the sense that he would have won if
all the third-party candidates, especially Ralph Nader,
had not run. (G.W.Bush was the official winner.)
Unfortunately again they failed to support this speculation
with any actual data.
It's plausible because when we check the official election results
we see their claim would have been true in
if ≥50.3% of the 120428 voters
for non-Bush, non-Gore candidates would have
preferred Gore over Bush,
and would have been true
if ≥42.1% of the voters for non-Bush, non-Gore candidates would have
But what they left unmentioned is that
exists suggesting that John McCain would have been
"majority winner" USA-wide if he had continued running after losing
the Republican nomination (based on Gallup poll data
released 13 Dec. 1999 and then confirmed by a second Gallup
poll in late Feb. 2000) in the sense he would have defeated Gore, Bradley,
and probably (based on indirect data) G.W.Bush head to head.
And Ralph Nader
was "majority winner" in the sense he did defeat
all three major
rivals Buchanan (659-240), Gore (527-500), and Bush (562-491) pairwise
among the sample studied by the "American National Election Study"
using essentially the voting system Maskin & Sen suggest below
provided we only consider voters who scored both
candidates in each pair.
This all is quite different from what most readers would have inferred by
Fact check #3:
Maskin & Sen claimed Egypt's 2012 election of Muslim Brotherhood
candidate M.Morsi was a mere plurality win
which "helped to undermine democracy in Egypt altogether."
Congratulations M&S; this time we actually wholeheartedly
agree with one of your claims, and unlike you,
we have data to back it up.
M&S's suggested voting system:
Maskin & Sen therefore suggested that the Republican Party
instead should have
counted votes via a "Condorcet method." Specifically:
Maskin & Sen's votes would have been rank-orderings of the
22 to 25
candidates. If a voter left any
Republicans unranked, that would be interpreted as ranking
them all co-equal last.
The winner is the candidate who, based on those ballots,
would pairwise defeat any rival ("Condorcet winner").
If however, no Condorcet winner exists (which, as M&S
state, can happen), then M&S do not explain what to do then,
but suggest perhaps "a runoff between the two candidates who win the
most aggregate support in the pairwise comparisons."
What "aggregate support" might mean, they do not say.
M&S then clarify that "for simplicity" they were speaking about a
but say "Condorcet's prescription would also be applicable in
primaries where delegates are assigned proportionally." I have no
idea what they meant by that, and I defy them to produce any
citation to anyplace in all of Condorcet's writings, in which he explained
a way to use his method to "assign delegates proportionally."
Fact check #4:
M&S say "Kenneth Arrow's famous 'impossibility theorem'
demonstrates that there is no perfect voting system."
Actually, Arrow's theorem
never demonstrated any such thing, because it never said anything about
every voting system. It only said anything
about rank order voting systems, leaving
voting completely unaddressed (not to mention an infinite number of other
voting systems too). As Arrow himself fully admitted.
And indeed, as we demonstrated
(and as was also pointed out by M&S's fellow Nobelist John Harsanyi)
range voting actually accomplishes what Arrow's theorem
would have deemed "impossible,"
at least with some verbatim wordings of his theorem!
(It is not entirely clear how to interpret what Arrow's
theorem said, if it is applied illegally to non-rank-order systems,
but we are simply pointing out that with some verbatim wordings of this theorem
applied to range voting, we find range voting does satisfy every
single Arrow criterion despite the fact the theorem, if applicable,
would have claimed that impossible.)
It is unfortunate to see M&S once again perpetuating
this misinformation myth in a high-visibility media setting even 8 years after we
Maskin on exactly this same false statement.
It is especially depressing when we consider
the fact that Arrow was Maskin's supervisor as a grad student.
Fact check #5:
M&S say (correctly)
that their system could fail to produce a "majority winner."
A voting system that sometimes
fails to produce a winner, of course would be unacceptable for the GOP's
But M&S then reassure us that this would be "quite unlikely in practice"
giving (as usual) zero supporting evidence.
Well, the race that stimulated M&S to say all this
was the 2016 USA republican presidential primary, with
22 (or by some counts 25) candidates.
The reader might want to guesstimate for him- or herself:
What are the chances that among these 22 candidates,
one (call him X) exists (where M&S think X≠Trump)
who would have defeated each among his 21 rivals head-to-head?
X presumably isn't Cruz,
since Rubio defeated him 46:40 in the PPP early February poll,
and Kasich defeated him in every single-state pairwise poll.
Is X Rubio, who failed to carry even
his home state of Florida and still would have been crushed
by Trump there even with all other candidates gone?
Is X Kasich, who is currently officially in 4th place
and would be defeated head-to-head by Trump based on
the average of 3 nationwide pairwise polls?
Summary of checked facts:
out of Maskin & Sen's first 4 "facts" checking out,
we see they evidently have the same reliability as a coin toss.
My suggestion to M&S would be that they
make actual data – rather than fake data they dream up –
dominate their op-ed. That would be a superior approach,
even though it would require more work on their part.
What is wrong with M&S's suggested
voting system for the Republican primary?
First of all, no system is acceptable
if it is too complicated to describe, or if
its rules are nowhere described.
And M&S's rules are undescribed.
Think about that. Maskin had an entire
2004 Scientific American
article to describe his rules in.
He still was either unable or unwilling,
even in all that space, to explain his rules of who wins
with any given set of ballots in his voting system.
Why? Probably because Maskin felt that if he did explain the rules,
that description would be too complicated or too unappealing.
I also corresponded with Maskin at that time, complaining among other
things about exactly that. Twelve years later, I am still waiting
for Maskin to tell me his rules of how to determine the winning candidate from
the votes. Think about that. Even given 12 years to do it, and
given the chance to provide
his rules description to the best voting system website
on the planet, or in a full Scientific American article,
or in a paid and beautifully transcribed lecture, or in
a New York Times op-ed too, Maskin repeatedly didn't.
Further, M&S's op-ed's hints-about-their-rules
actually contradict Maskin's 2004 Scientific American piece's
hints-about-its-rules. Consequently we simply still do not know
what system they are "proposing."
It is simply not acceptable to propose a new voting system,
unless you propose a voting system. Maskin didn't.
The prospect of voters,
as their ballot, rank-ordering all 22 Republican candidates
(25 in some states), is not appealing.
That would be complicated, error-prone,
and unpopular. Don't believe me? OK, try it yourself.
Please rank-order all 22 Republican
(If you make any error, then
discard your entire sheet of paper and start again.
You are not allowed to erase marks on ballots, at least not in my state.)
In Australia, the country with more rank-order-ballot
single-winner voting experience than all other countries combined,
three polls in 1974, 1984, and 2010
that Australians, by 53-38, 54-39, and 57-37 majorities
(these each sum to less than 100% due to "don't know" answers),
wanted to replace their present rank-order voting system for
Australia's single-winner House elections, with plain plurality voting,
even though, on average, Australia
only asks them to rank-order about 7 candidates,
In San Francisco,
after switching to rank-order ballots in 2004,
error rate rose by a factor of 7
and 12.9% of voters
they "did not understand" the voting system.
Follow-up polls of San Franciscans 10 years later then
showed they believed switching to
the new voting system had been a mistake.
The prospect of a runoff second Republican nominee battle
also seems unappealing.
With M&S's rules voters are allowed to leave candidates unranked,
whereupon all the unranked ones are automatically "ranked" co-equal last.
That policy is extremely distortionary. Probably most voters
most of the time leave candidates unranked due to lack of familiarity
with Jim Gilmore or Jack Fellure, not because they consider them
worst. M&S interpret this non-data – which
quite likely in its shear bulk would outweigh the actual ballot data!
– in the most-distorted way they possibly could. That is not wise.
In addition to being unwise, it makes it almost certain that no
be able to attain majority support with their system.
For example if each voter ranked 10 of the 22 candidates,
and the 12 unranked ones were randomly-uniformly selected,
then it would
be mathematically impossible for any candidate to be a "majority" winner,
at least under the usual interpretation that when 54.5% of
voters rank you "the worst" you cannot be a "majority winner."
That would mean that M&S's failure to describe the rules for
choosing a winner in that case, would actually dominate the picture!
So their "proposal" is a system which, the vast bulk of the time,
either has no rules, or certainly would not yield a "majority" winner –
making their very name misleading, and mooting the entire goal of their method.
As we pointed out above, Ralph Nader was the "majority winner" in 2000
(according to ANES poll data and M&S's voting system rules)
even though he got only 2.74% of the official vote. That huge discrepancy
proves that an enormous fraction of votes are "strategic," i.e, dishonest.
(Indeed the same study found that over 90% of honestly Nader- and Buchanan-top voters
in 2000 actually voted for somebody else. I repeat: 90% dishonest voting.)
What effect would strategic voting have on M&S's voting system?
They do not even consider this question. However, the "DH3 pathology"
is one common example of the sort of mess that M&S's voting system could
get itself into with strategic-exaggerating voters:
M&S's system automatically elects the candidate whom all voters unanimously agree is the
worst, in any scenario where (a) there are 3 kinds of voters: A-fans, B-fans, and C-fans,
in roughly equal numbers; (b) there is at least one other candidate W they all agree to be
worse and hence not in contention; (c) the voters naively strategically exaggerate
in their votes to try to "make them have more impact" by claiming their favorite
candidate is best and his 2 main rivals "worst".
This is a very common scenario.
The result it yields is worst possible.
Also, more generally, with M&S's system it is rather tempting for voters simply to
rank one candidate – thus automatically ranking all 21 others "co-equal bottom."
That gives you (or it naively appears to)
more power than any voter who sincerely ranks all the candidates, and certainly it is
If voters voted this way, then they'd be casting old-style plain plurality votes,
and M&S's "improved" system would be moot.
We would like to suggest a simpler proposal for the Republican primaries,
not to mention other elections:
The rules of our systems are much simpler (and fully describable!).
There is no possibility, at all, of a "cyclic" no-winner scenario.
No "runoff" second round is needed.
It is a proven theorem
that, under certain simple assumptions about voter strategic behavior,
these systems will elect a "majority winner" whenever one exists.
In other words: with our proposal: strategic voting actually helps
elect an honest-votes
majority winner, unlike with M&S's system where it hurts.
This makes it plausible (and
this suspicion has been
confirmed in computer simulations)
that, paradoxically, our proposal will actually elect
"honest votes majority winners" more often than M&S's
more complicated proposal,
even though the latter was specifically designed to do that!
In other words, M&S's very own goal appears better satisfied by
our proposal than theirs.
However M&S's goal was the wrong goal. The correct goal is to
maximize society-wide utility. (This correct goal can contradict the correlated, but wrong,
goal of electing a "majority winner.")
That correct goal, in computer
simulations ("Bayesian Regret")
is achieved better by score voting than by any rank-order-based
system tried, and robustly when the numbers of voters and candidates are varied,
and when different voter-strategy/honesty mixes and underlying scenario generators
Surveys have shown that
score-voting rating ballots, and approval ballots
(and plain-plurality ballots!),
over rank-ordering ballots.
Also voters find them more
and take less time to fill out
With score ballots, a voter who leaves a candidate unscored does
not have her score magically transmuted to
rating him co-equal worst. Unscored means unscored.
If the voter wants to rate somebody worst, she can do so explicitly.
With score voting, voters can express not only preferences, but strong
and weak preferences.
There has been a great deal of approval-style polling in both
the present election, and many past elections. (Far more
than the amount of pairwise polling, and especially of
all-pairs pairwise polling, which is virtually unheard of.)
These polls clearly show that
Trump will be the least-approved major-party's US presidential candidate ever,
also are majority-disapproved.
also is disapproved by more people than approve him,
each enjoy more approval than disapproval.)
They also allow us to estimate
how well various candidates would
have done in past elections if they had employed
approval voting, or sometimes score voting.
(For example, in
Egypt 2012, a secular moderate
would have won the presidency.) This is unlike the situation with
Condorcet-style voting, where we are operating in a state of ignorance.
We also point out that there are good reasons pollsters have conducted a lot
of approval-style and score-style polls, but they never, or almost never,
conduct Condorcet-style polls. Perhaps, if Maskin and Sen want to be political scientists,
they should ask themselves why 100% of the professional experimentalists, i.e. pollsters, in this
area, are making that choice.
Approval and score voting have actually been used
to elect the top politicians of several countries
for periods ranging from many decades to centuries.
Greece 1864-1926; the catholic Pope, who was head of his own large state, 1294-1621.)
They appear to have worked ok, apparently better than either
plurality or instant runoff.
Indeed, Sparta and Venice were among the best countries on Earth during their times
(at least from the point of view of their voting classes) and thrived despite
severe inherent disadvantages; Catholicism was the most successful religion
judged by sheer numbers, during that era; and Greece improved itself during
its approval voting era from a corrupt bankrupt failed state into a notable power.
no country has ever used a Condorcet method to elect anybody
important – or if one ever did, then Maskin and Sen, in all their writings,
have failed to find it!
Score voting has been shown
essentially equivalent to the system used by honeybees
(apparently the world's most experienced democrats). The honeybees could have used
other systems such as Plurality, Approval, Borda, instant runoff, or Condorcet.
But they didn't. The reason they didn't was: millions of years of evolution was unable to
find any alternative system that both gave them better survival chances, and was simple enough
for bees to use.
With score and approval voting, if candidate X is the winner in the North, and also in
the South, then
X is guaranteed to be the winner in the whole (North+South combined) country.
But with M&S's system, this "partition consistency" is
guaranteed to fail in some elections (theorem by Young).
With score and approval voting, casting an honest vote can never hurt you,
in the sense that it cannot cause the election result to worsen from your point of view
versus if you had not voted. (At least, when scoring all candidates is demanded.)
But with M&S's system, this "participation" property is
guaranteed to fail in some elections
(even if ranking all candidates is demanded).
That renders the meaningfulness of your vote, and the usefulness of voting,
and the legitimacy of that election result, all somewhat suspect.
With score and approval voting, giving your favorite candidate the maximum possible
score, can never hurt you. I.e, those systems guarantee that
you always can cast a ballot that max-scores your favorite,
without ever worsening the election result versus if you had cast a ballot
that dishonestly "betrayed" your favorite.
In contrast, M&S's system is guaranteed to fail that property – there
will always be election situations in which voters must betray their favorite to get
the best attainable election result.
Systems in which voting for your favorite is anti-strategic, are suspect.
In the present-day USA and Australia,
the most blatantly obvious and enormously damaging consequence
of strategic exaggeration-voting
is two-party domination. That is, voters regard the two major-party
candidates (call them A and B) as having the best chances to win. Therefore they exaggerate their
true feelings in their votes, pretending A is "best" and B "worst" (or the reverse).
It is a mathematical theorem that if at least 67% of voters
do this in either
the USA's plurality-voting system,
(used to elect its House) instant runoff voting system,
then no third-party candidate can ever win. And sure enough,
both the USA and the Australian House have developed enormous 2-party domination.
With M&S's system, third party victories are impossible if 100%
of voters employ this "naive exaggeration strategy." (Experimentally,
in the USA about 98% and in Australia about 85% of voters vote in this exaggo-style.)
So it is plausible that M&S's system still will engender 2-party domination.
Meanwhile, with approval and score voting, even if 100% of
voters vote in naive-exaggo-style, it still remains entirely possible
for third-party candidates to win. That provides hope of escaping 2-party domination
so that there can actually be a democratic "marketplace."