A third criterion, however, does differentiate between the two. Neutrality, as this axiom is called, has two components. The first is symmetry, which means that the electoral rules should not favor one candidate over the other. The second requires that the voters’ choice between candidates A and B should not depend on their views about some third candidate C. What would happen in our U.S. example if the Bush voters’ ranking shifted to become Bush, Gore, Buchanan, Nader (instead of Bush, Buchanan, Gore, Nader)? From the standpoint of true majority rule, nothing important would change: the majority still prefer Gore to Bush. But look at what happens under rankorder voting: Gore now receives 348 million points, while Bush’s total remains 346 million. Gore now wins instead of Bush.
Obviously, rank-order voting can violate neutrality. Voters’ preferences between Gore and Buchanan, a candidate who stands no chance of getting elected, determine the choice between Bush and Gore—and the outcome of the election. In contrast, true majority rule always satisfies neutrality. This last assertion may puzzle those readers who recall that in the actual election, discussion abounded about whether votes for Nader would affect the race between Bush and Gore. Indeed, in retrospect it appears that Nader—perhaps with help from the infamous butterfly ballot in Florida and even from Buchanan—may have siphoned off enough Gore votes to tip the election to Bush. But this effect was possible only because the U.S. election system is not actually true majority rule but its own unique system.
Majority Rule and the French Election
LET’S LOOK AT WHAT would happen to the French election of 2002 under true majority rule—which, for simplicity’s sake, we will henceforth refer to as majority rule. Imagine Chirac, Jospin and Le Pen are the only candidates, and the electorate divides into three groups. Everyone in the first group, 30 percent of voters, has the ranking Jospin, Chirac, Le Pen. In the second group, 36 percent of the electorate, the ranking is Chirac, Jospin, Le Pen. In the remaining 34 percent, voters rank Le Pen over Jospin over Chirac. Chirac and Le Pen—with 36 and 34 percent of the vote, respectively—would move forward into a runoff, where Chirac would easily prevail because 66 percent of voters prefer him to Le Pen.
The same outcome would result under yet another system, called instant-runoff voting (IRV), which is practiced in Ireland and Australia and which, like rank-order voting, has been advocated as an alternative to the French and U.S. systems. In IRV, simply put, rankings are used by election officials to successively eliminate the lowest-ranking candidates (and to incorporate their percentages into the voters’ next-ranked choices) until only two candidates remain.
But the French and IRV systems conflict with majority rule. If you examine the configuration of voters’ rankings, you see that Jospin actually commands an enormous majority: 64 percent of the electorate prefer him to Chirac, and 66 percent prefer him to Le Pen. Majority rule dictates that Jospin should win by a landslide.
Recall that under majority rule a voter can make a political statement without harming the chances of any electable candidate. Someone who preferred Jospin to Chirac and knew that Le Pen had no chance of winning but wished to rank him first as a gesture of protest could do so without fear of knocking Jospin out of the race. (Except, of course, in the highly unlikely event that a majority of other voters made the same gesture.) The analogous point can be made about a voter who preferred Gore to Bush but wished to lend symbolic support to Nader. Yet despite these virtues, majority rule has a flaw. It can violate another well-accepted voting principle: transitivity. Transitivity requires that if candidate A is chosen over B, and B is chosen over C, then A should be chosen over C. Now, ignoring Buchanan, pretend that 35 percent of the electorate prefer Gore to Bush to Nader, 33 percent rank Bush above Nader above Gore, and 32 percent go for Nader above Gore above Bush. Sixty- seven percent of voters rank Gore above Bush, 68 percent rank Bush above Nader, and 65 percent rank Nader above Gore. In other words, no matter which candidate is chosen, at least 65 percent of voters prefer somebody else! In this case, majority rule produces no winner.
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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