Ranking Candidates Is More Accurate Than Voting

A ballot-counting system that allows voters to rank the candidates could provide more accurate results

On the other hand, the American Constitution stipulates that, absent a majority of the electoral votes, the House of Representatives should determine the winner. With a Republican majority in 2000, the House would presumably have gone for Bush. Clearly, having U.S. voters name solely their favorite candidate does not result in an outcome that is obviously right. As in the French election, such ambiguity can be resolved by having voters submit complete rankings. Even though Gore is the favorite of only 49 percent of the electorate, the rankings show that a clear majority of 51 percent—the Gore and Nader voters combined—prefer Gore to either Bush or Buchanan. So Gore is the winner according to an electoral system called true majority rule (or simple majority rule), in which voters submit rankings of all the candidates and the winner is the one who beats each opponent in head-to-head competition based on these rankings.

Rankings can also be used in other electoral systems. Consider, for instance, “rank-order voting”—a procedure often used to elect committee officers that has been proposed to solve the problems inherent in the American and French presidential electoral systems. If four candidates are running, each voter assigns four points to his or her favorite, three to the next favorite, two to the next, and one to the least favorite. The winner is the candidate with the biggest total. The method appears to have been invented by Jean-Charles Borda, an 18th-century French engineer, and is sometimes known as the Borda count. Imagine that 100 million people vote in the U.S. election. Based on our earlier assumptions, we know that 49 million of them will rank Gore first. So Gore will receive 196 million points—that is, 49 million times four points—from the Gore voters. The Nader voters place him second, so he picks up six million points from them. Finally, the Bush and Buchanan voters place him third, for an additional 98 million points. His grand total is 300 million points. If we make the corresponding computations for the others, we find that Nader gets 155 million points and Buchanan 199 million. Strikingly, Bush gets 346 million, even though a majority of the electorate prefer Gore. Only 2 percent of the electorate ranks Bush lower than second place, which is good enough to elect him under rank-order voting.

Thus, true majority rule and rank-order voting result in dramatically different outcomes. Considering this sharp contrast, it may seem hard to say which method is better at capturing the essence of voters’ views. But we propose to do just that. We can evaluate these two systems—and any other—according to some fundamental principles that any electoral method should satisfy. Kenneth J. Arrow of Stanford University originated this axiomatic approach to voting theory in a 1951 monograph, a work that has profoundly shaped the voting literature.

Most voting analysts would agree that any good electoral method ought to satisfy several axioms. One is the consensus principle, often called the Pareto principle after Italian sociologist Vilfredo Pareto. It states that if everyone agrees that candidate A is better than B, then B will not be elected. This axiom does not help discriminate between true majority rule and rank-order voting, however, because both methods satisfy it— that is, both will end up with B losing. Moreover, the principle does not apply very often: in our U.S. election example, there is no unanimous preference for any one candidate over another.

Another important axiom holds that all voters should count equally—the “one-person, one-vote,” or equal-treatment, principle. Voting theorists call it the principle of anonymity: who you are should not determine your influence on the election. True majority rule and rank-order voting also both satisfy anonymity.

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1. 1. Tom_B 12:38 AM 10/8/08

If the election is as close as the Bush/Gore election, there obviously is a serious question about who will do a better job. So splitting hairs about who has a tiny bit more support/trust does not seem all that useful. What we really need is an efficient system to recall someone who is not doing a good job. That is one whose performance is highly unpopular with the people who elected him, not the "high crimes and misdemeanors" law we have now. Something like the recall law for the California Governor. I notice that once the new Governor (Schwarsenegger) realized he could be voted out, he changed his behavior to improve his popularity. Perhaps an election should be called if the official's popularity rating falls below something like 50% for six months. (If he cannot even keep half of the people happy, he is not doing what needs to be done). Things happen much faster now than they did 200 years ago. We cannot afford to have an elected official be allowed to mess things up for years before a change is made.

2. 2. RichardCampbell 01:04 PM 10/8/08

Does not Wisdom call?

3. 3. RichardCampbell 01:34 PM 10/8/08

This is not exactly a new thing. Something very much like this (as I understand the essence of the authors thrust) was used in the General Election of 1952, British Columbia, Canada.

It appears that people, aware of the risk of their ideological foe being elected under the new system, chose the third choice candidate as a spoiler vote. That way, the third place choice ended being elected.

On the other hand, it could be argued in light of many successive wins, that the electorate was undergoing a transition to a new (to them) political party that was more in line with the electorate's values, an alienation from the long standing traditional expressions of liberalism and conservatism of the day that echoed the national party systems that were perceived as largely uncaring of regional concerns.

Either way, this electoral system appears to have been deemed by the winners to be too unpredictable a method to guarantee a re-election and was not used again.

http://www.nationmaster.com/encyclopedia/British-Columbia-general-election,-1952

It seems clear that when given a two part choice, a partisan electorate will often choose to vote strategically, rather than logically: ie. A=45%, B=45%, C=10% popular. Voting day choices are:
Love A, hate B, C has no chance=vote A,C
Love B, hate A, C has no chance=vote B,C Love C, hate B, hate A less=vote C,A
Love C, hate A, hate B less=vote C,A

Result is C wins

I would interested as to how such a counterproductive tendency might be factored out.

4. 4. RichardCampbell 01:41 PM 10/8/08

Correction:

It seems clear that when given a two part choice, a partisan electorate will often choose to vote strategically, rather than logically: ie. A=45%, B=45%, C=10% popular. Voting day choices are:
Love A, hate B, C has no chance=vote A,C
Love B, hate A, C has no chance=vote B,C
Love C, hate B, hate A less=vote C,A
Love C, hate A, hate B less=vote C,B

Result is C wins

-------------------

ps, to the forum master, I find the pale grey font hard to work with. I had to go back and resubmit owing to a typo

5. 5. minulescu in reply to RichardCampbell 10:20 PM 10/8/08

How about a system where candidates get rated on a 1-10 scale lets say.
By popularity, its A=46%, B=44%, C=10%

However, the people that prefer A, prefer A by a small margin, while the people that prefer B, definitely don't like A.

In essence, in this case, my opinion is that B should win. Such a rating system would allow that.

100 hundred people vote:
The ppl that prefer A (46%), might vote, on average A=7 B=6 C=2
The ppl that prefer B (44%), might vote, on average A=5 B=8 C=2
The ppl that prefer C (10%), might vote, on average A=2 B=2 C=8

Then you have:
A: 7*46% + 5*44% + 2*10% = 5.62
B: 6*46% + 8*44% + 2*10% = 6.48 (B is the winner)
C: 2*46% + 2*44% + 8*10% = 2.6

That makes sense to me! What do you all think? Is my logic wrong anywhere? Are there cases where the result wouldn't be representative of what the people want? (I haven't though deeply about this, just on the whim).

This should work extremely well in bi-partisan case of America, where MANY republicans will vote republican, even though they like the Democrat almost just as much...but they are Republican so they have to go with that. Or vice versa of course. Thus, this system will reveal what the people really want. No?

6. 6. fmerchant 02:33 AM 10/9/08

Hey Richard Campbell,

To be able to factor out the tendency to select C from the above example, the correct approach would be to allow for higher weight to be assigned to the preferred choice. For example initially you would have done the following,
Love A, hate B, C has no chance= A:2 and C:1
Love B, hate A, C has no chance= B:2 and C:1
Love C, hate B, hate A less=C:2 and A:1
Love C, hate A, hate B less=C:2 and B:1

Instead if the following approach is utilized a better result is attained.
Love A, hate B, C has no chance= A:3 and C:1
Love B, hate A, C has no chance= B:3 and C:1
Love C, hate B, hate A less=C:3 and A:1
Love C, hate A, hate B less=C:3 and B:1

Now when you tally the votes you get a the winner as either A or B (depending on the proportion split for the 10% who love C). The solution is also scalable, in the case where you have 4 candidates, you would select 5, 3, 1, and 0 and so on. The provides a deterrence for the second and third place votes and justifies a higher weight for the first choice, which accurately accounts for the voter's intent.

Hey minulescu,

I think that in your example, those who prefer C should also end up adding to 15, right now A=2 B=2 and C=8 where 2+2+8=12 but for those who prefer A and B the total sum is 15. Moreover, I think that it would be very difficult to expect voters to come up with the proportional split between A, B and C. This would have to be internal to the algorithm or the system, the voters I believe can only be expected to provide their rankings, asking them to do more would be too hard to track and slow down the voting process.

Faheem Merchant

7. 7. radioactiveboyscout 11:22 PM 10/11/08

I have seen much discussion on our electoral system since the Bush/Gore election. One of the points that the articles seem to miss is the what the underlying principle of the electoral system is. The assumption is the articles that I have read always seem to be that the popular majority should pick the winner. I was taught at a young age that the purpose of the electoral system was that no one major constituency could always win the election. Many of the articles I read seem to imply that this is bad. But doesn't this prove to be good in that no major constituency can always reign supreme, thereby disenfranchising smaller groups. It sort of forces our system to be somewhat progressive. Doesn't this have virtue?

8. 8. Ian St. John 10:03 AM 10/13/08

Rank Order has potential. However, how it operates is crucial.

I propose the following.

The first pass determines one 'loser'. That persons vote is eliminated and shifts to the second choice. Then with this 'vote shift' another 'loser' is chosen, again shifting all that are currently aligned to that candidate to the next on the list.

When this process ends with one candidate left, you have the Candidate that is most favored by the most people.

9. 9. Ian St. John 10:05 AM 10/13/08

Rank Order has potential. However, how it operates is crucial.

I propose the following.

The first pass determines one 'loser'. That persons vote is eliminated and shifts to the second choice. Then with this 'vote shift' another 'loser' is chosen, again shifting all that are currently aligned to that candidate to the next on the list.

When this process ends with one candidate left, you have the Candidate that is most favored by the most people.

10. 10. RetiredUSNChief 09:18 AM 10/9/09

Once upon a time, Scientific American had an article about the mathematics of how the Electoral College works and why our founding fathers settled on that particular system.

It was published in the mid-1990's sometime, but I don't remember exactly when and I no longer have it. I'd sure love to re-read it in light of some of the other articles Scientific American has published since.

11. 11. AmazingBlair in reply to Ian St. John 01:41 PM 7/15/12

To Ian St. John:
I think the process you describe is the Instant Runoff Voting (IRV) method alluded to briefly in this article. It is in use in Australia and seems quite sensible.

-Blair

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