With voters’ rankings belonging to this two-element class, rank-order voting satisfies its nemesis: the principle of neutrality (because voters’ views on Nader do not affect whether Bush or Gore wins a rank-order election). Yet majority rule also works well here, because it satisfies its nemesis, transitivity. But rank-order voting no longer works well if the situation becomes slightly more complicated. If we add a third ranking— Gore, Nader, Bush—majority rule is still transitive. These three rankings together do not constitute a Condorcet cycle. Rankorder voting, however, no longer satisfies neutrality. Suppose 51 percent rank Bush above Gore above Nader. If the remaining 49 percent rank Gore above Nader above Bush, Gore will win. If the remainder instead have the ranking Gore, Bush, Nader, however, then Bush wins—even though this group of 49 percent has the same ranking of Gore and Bush in either case.
Majority rule still fails to work well sometimes, as the Condorcet paradox shows, though less often than other voting rules do. And in such cases, it has to be modified to identify a winner. There are many ways this can be done. Perhaps the simplest modification is as follows: If no one obtains a majority against all opponents, then among those candidates who defeat the most opponents in head-to-head comparisons, select as winner the one with the highest rank-order score.
Improving Future Elections
THE WAY most countries pick their presidents is faulty. Both the 2000 U.S. and 2002 French presidential elections were appreciably affected—perhaps decisively—by candidates who had no realistic chance of winning. These candidates were able to wield influence because, in each case, only a voter’s top-ranked candidate was counted.
We believe that when more than two choices present themselves, voters should submit a ranking of candidates and that majority rule—as we have discussed it—should determine the winner. Such a method would not be perfect; no method is. But as the majority dominance theorem shows, it would come closer to an accurate representation of the voters’ wishes than any other system does.
This story was originally published with the title "The Fairest Vote of All"
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11 Comments
Add CommentIf 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.
Reply | Report Abuse | Link to thisDoes not Wisdom call?
Reply | Report Abuse | Link to thisThis 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.
Reply | Report Abuse | Link to thisIt 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.
Correction:
Reply | Report Abuse | Link to thisIt 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
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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
How about a system where candidates get rated on a 1-10 scale lets say.
Reply | Report Abuse | Link to thisBy 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?
Hey Richard Campbell,
Reply | Report Abuse | Link to thisTo 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
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?
Reply | Report Abuse | Link to thisRank Order has potential. However, how it operates is crucial.
Reply | Report Abuse | Link to thisI 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.
Rank Order has potential. However, how it operates is crucial.
Reply | Report Abuse | Link to thisI 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.
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.
Reply | Report Abuse | Link to thisIt 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.
To Ian St. John:
Reply | Report Abuse | Link to thisI 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