How to Rig a Majority Vote


Voting is supposed to be about getting what
the majority wants. But that is not always the way it works. Let’s imagine that you and
your two friends Jim and John are on your way home from a party. The three of you want
to get something to eat before you head home. All three of you immediately call out a different
preference, so there is no clear majority in favor of any option. But all of you want
equal say in the decision about where to eat. So you propose voting on two options at a
time to figure out what the group’s preferences are. So you first say, “Tacos versus burgers
– which do you guys want?” Personally, you want pizza more than anything, but you’d also
be alright with tacos. Burgers sound awful right now. So you vote tacos. Jim he votes burgers. John
votes tacos. So tacos are the clear winner. But since pizza wasn’t even on the table for
the last vote you ask for another round of voting to see how pizza ranks against the
current winner. Your friends agree. In this new matchup tacos versus pizza you obviously
vote for pizza. Jim also votes for pizza. John is left as the only person who would
prefer tacos to pizza. So pizza appears to be the new champion. You’re thrilled. But now Jim is not happy. He says, “That is
not fair. We decided that tacos win out of burgers and pizza wins out over tacos, but
how do you know that there is not a majority in favor of burgers over pizza. We never voted
on that.” You counter, “That doesn’t matter. We already voted on burgers.” But Jim doesn’t budge, so to make him happy
you agree to have one last vote – burgers versus pizza. You of course vote for pizza.
Jim votes for burgers like you expected, but now John also raises his hand in favor of
burgers. So burger are declared the winner. What happened? Well, let’s look at everyone’s preferences
again. As you can see, the problem is no one ranks any of the options in the same order,
so even though a vote between any two options yields a winner, between all three choices
it is impossible to achieve a consistent outcome. This is called Condorcet’s Paradox. In this scenario voting will result in what
we called a cycle, so after voting on two pairings you may seem to have a clear answer,
but if you change the order in which you voted on the pairings you would get a completely
different result. None of the three options is preferred by a majority of the voters,
and voting cannot resolve the problem. If you are surprised by this let me take you
one step further. The fact that any outcome may be possible
implies that whoever gets to decide the order of the options is really the one who picks
the outcome. This person is called the agenda setter. If the agenda setter is savvy and
if he has any inkling of the relative preferences of the other voters, he can change the order
of voting to achieve his preferred outcome. If you had been savvy you would have made
the last vote tacos versus pizza and you would have gotten what you wanted. But would that
have been fair? The Condorcet Paradox shows that taking a
vote will not always select what the majority prefers. In fact, when an agenda setter manipulates
the voting process he is the one who will decide what the group does.

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Comments

  1. Run-off voting systems and "blanket primary" systems can lead to all sorts of lousy match-ups. In 1991 in the Louisiana Governor's Election, the state's blanket primary system ended up with the vote being split by a laundry list of candidates in the first round causing Edwin Edwards, a former governor who had been accused of bribery to end up in a run-off against David Duke, an Imperial Wizard of the Klan (Edwards won). Blanket primary elections also sometimes lead to situations where 1 party has several candidates, the other has 2 and the party with several candidates splits their vote so much that the party with 2 candidates wins the plurality resulting in 2 Republicans or 2 Democrats facing each other in the run-off.

    We've seen screwy run-off elections elsewhere too. In the 2002 French Presidential Elections Jacques Chirac was the only center-right candidate and a member of the Union for a Popular Movement party. The various center-left, leftist and social democracy parties all split each other's votes. Chirac ended up in a run-off against Jean-Marie LePen of the National Front party, a neo-fascist party representing Vichy regime rejects (Chirac won easily).

  2. Question, this is kind of a like a rock-paper-scissors thing. But in real life there aren't 3 completely different parties. There are only 2 different ways you can go, left or right. In politics, there could be a more center one. So lets say that there's parties left right and middle. Party left obviously likes their party the most, but is closest to the middle. Same with the right, they like the right the most but are closest to the middle. This real life application is different b/c in rock paper scissors, rock doesn't beat scissors AND paper, just one. In the real world, left and right are both closest to the middle. Correct me if I'm wrong, but isn't this an incorrect example? 

  3. I'm not convinced. Seams more like this is trying to imply that voting is the same as rock paper scissors, with exactly one third being rock (with paper then scissors as their ensuing alternatives), 1/3 being paper (with scissors then rock as their ensuing alternatives), and 1/3 being scissors (with rock then paper as their ensuing alternatives). What about a person with the descending (most to least) preferences: scissors then paper then rock? It doesn't seam applicable to a large population.

  4. This describes the present WEAK DEMOCRACY of US-CANADA-UK-FRANCE duopoly. In the republican form of gov't electors dictate laws & policy no need for any voter input in direct democracy another WEAK DEMOCRACY tactic. 

  5. Some have suggested Mandatory Voting:
    …which means to say that it will be our peers who can't watch an educational International Space Station video without vectoring on the first lens-flare or window smudge as their ''proof'' that little green space aliens have established pro-bono-proctology sausers outside most of our nations trailer parks will become the major demographic 'AKA; voting pool' that suits in Washington will be throwing campaign-bribe-bananas to under the the assumption that they can assemble some random Shakespeare play by throwing feces at voting booths?
    …and just like that snaps finger and our space program begins to parallel plot-lines of a typical Scooby-Doo episode simply by demanding its viewers to tear their attention away long enough to press buttons determining NASA's next course of action…just think what it can do for overturning all these decades of living under the harsh and primitive conditions Americans presently have in thinking and doing for themselves.

    …no…what we need are conscious voters…but that demographic is fast evaporating into the matrix. The cure for this issue is not more numbers…it is accurate numbers…and the only thing brain-dead votes are good for is in deepening our collective national coma. 

  6. Voting is nothing else but using the force of the government to violate the rights of your neighbors, and gives you a real sense of belonging and community.

  7. this can be redone much better. use the primary process in caucus states where delegates are selected to go to the level of voting several times. the winner at the end of the process might not have even been in the top 3 of initial voting.

  8. I disagree that voting is about getting what the MAJORITY WANTS. I think voting is to determine what EVERYONE wants and then we have a discussion about how we can make a decision that everyone can live with.

  9. Maximal lotteries deals with this in an elegant way. http://dss.in.tum.de/files/brandt-research/fishburn_slides.pdf

  10. Interesting! perhaps you may be interested by this popular video (in French) describing voting paradoxes and a solution to overcome them:

    https://www.youtube.com/watch?v=ZoGH7d51bvc&feature=youtu.be&ab_channel=ScienceEtonnante

    Majority Judgment is developed in detail in this MIT book: http://mitpress.mit.edu/books/majority-judgment

    I am one of the authors (sorry!)

  11. Why not mentioning the Majority Judgement, created by scientists and mathematicians to vote better?! Mainly we talk about Michel Balinsky or Rida Laraki (I'm not sure I'm writing their names properly).

    Thank you!

  12. Good video, but you should have suggested at the end that score voting is the most likely system to not suffer from this problem and how it can easily 'unsplit' such voting situations.

    In a nutshell, Kenneth Arrow showed in the 1950s that ranked voting (of which this video is an example) is undemocratic and that only score voting gets anywhere near to a true democracy.

    Every problem in modern politics is a result of us using ranked voting over score voting: every split vote, every lesser of two evils, every centred-squeezed government whose preferences are the opposite of ours.

    There's no point in complaining about Clinton/Trump/May/Corbyn/etc if you're not prepared to fix the central problem that puts (or doesn't put) them into power in the first place.

    Support Approval Voting and STAR Voting if you want real positive change.

  13. This video highlights the problems of forcing decisions to be binary. If you insist there are only two choices then a surprisingly large fraction of people may be guaranteed to not get what they want. This is why we must break the hold the two major parties have on American politics. If third parties and independents were considered viable by the public it is much more likely that Americans could actually be happy with their elected officials.

    Any argument that 3rd parties are not viable ignores American history. The Republican party was founded in a schoolhouse in 1854 but in the 1860 election it took majorities in both houses of Congress AND the White House. In an era with no internet, no mass media, and where the speed of communication was defined by how fast you could ride a horse there, an upstart political party went from a couple dozen anti-slavery activists to the dominant party in America in just 6 years. In the 21st century it could happen in one election cycle if people would form their own opinions instead of making themselves into subjects of their chosen party.

  14. I vote that they all eat top ramen for 6 months, save their money then chip in to build a restaurant that sells tacos, pizza and burgers.

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