Win, Place, and No!

How the dismal science applies to your life.
Feb. 6 1999 3:30 AM

Win, Place, and No!

The only truly fair election is the one with one voter.

18000_18847_neubecker_twisted1

Sandra Loosemore, CBS SportsLine's figure skating writer, has a mission. She wants to overturn the sport's new scoring system.

Advertisement

The traditional system came under fire after the Great Flip-Flop of 1997 at the European Championships. In the men's free-skating event, five competitors had skated, and the first three places were held by Alexei Urmanov, Viacheslav Zagorodniuk, and Philippe Candeloro, in that order. The final contestant, Andrejs Vlascenko, placed dead last--but in the process he managed to bump Candeloro up to second place, denying Zagorodniuk a silver medal.

(For Loosemore's explanation of how the old scoring system worked, and how it caused the Great Flip-Flop, click here.)

International Skating Union Chairman Ottavio Cinquanta decreed after the championship that the scoring system must be revised to prevent flip-flops. When the new system was announced in July 1998, Cinquanta rejoiced that the problem was solved, so that henceforth "if you are in front of me, you will remain in front of me."

Loosemore has raised several cogent objections to the new system. First, it is more complicated than the old system. Second, contrary to Cinquanta, it won't stop flip-flops. In fact, Loosemore's computer simulations suggest that it will make flip-flops more common, not less.

What should the ISU do? Economist Kenneth Arrow hacked this problem five decades ago with his "Arrow Impossibility Theorem," which proves that no reasonable scoring system can preclude flip-flops. (The word "reasonable" incorporates the ISU's commitment to basing final outcomes only on the order in which the judges have ranked the contestants rather than on their explicit numerical scores.)

When Arrow was laying the foundations for his future Nobel Prize, he was concerned not with ranking figure skaters but with ranking social priorities. But Professor Michael Stob of Calvin College points out that the problems are identical. Judges may disagree about whether Zagorodniuk is better than Candeloro. Voters may disagree about whether a Star Wars defense system is better than a tax cut. In order to name winners, the ISU needs a scoring system to amalgamate the judges' opinions into a single ranking. In order to take political action, the United States needs a social choice mechanism to amalgamate voters' many preferences into a single list of priorities.

It might appear that the United States can afford more ambiguity than the ISU. Members of Congress can get away with cheerfully endorsing multiple conflicting goals and declaring them all "top priorities," whereas at the end of the day, the ISU must declare who gets the gold, who gets the silver, and who gets the bronze. But the fact is that at the end of the day, political decisions do get made, as surely as skating medalists get chosen. The government either cuts taxes or it doesn't. Although the political process is far more complex than anything the ISU might devise, the decisions it arrives at are just as unambiguous.

Arrow set forth two desiderata for any social choice mechanism. First, unanimity, when it occurs, should be respected. If all the judges rate Zagorodniuk ahead of Candeloro, then Zagorodniuk should come in ahead of Candeloro. If 100 percent of the voters prefer Clinton to Dole, then Dole should not be president. This criterion is the easy one. I doubt that any sport, or any polity, has ever violated it.

Arrow's second dictum is that there should be no flip-flops. If A ranks ahead of B, then the entry of a third candidate, C, should not overturn that ranking. Simple majority voting, for example, notoriously violates the no-flip-flop criterion. It's easy to imagine an election where Clinton is initially ahead of Dole, but a third party entry by, say, Jesse Jackson, pushes Dole ahead of Clinton. This can happen even when Jackson runs a distant third, as long as he takes more votes from Clinton than from Dole. Arrow's goal was to eliminate such anomalies with a more sophisticated voting system.

TODAY IN SLATE

Politics

Smash and Grab

Will competitive Senate contests in Kansas and South Dakota lead to more late-breaking races in future elections?

Stop Panicking. America Is Now in Very Good Shape to Respond to the Ebola Crisis.

The 2014 Kansas City Royals Show the Value of Building a Mediocre Baseball Team

The GOP Won’t Win Any Black Votes With Its New “Willie Horton” Ad

Sleater-Kinney Was Once America’s Best Rock Band

Can it be again?

Technocracy

Forget Oculus Rift

This $25 cardboard box turns your phone into an incredibly fun virtual reality experience.

One of Putin’s Favorite Oligarchs Wants to Start an Orthodox Christian Fox News

These Companies in Japan Are More Than 1,000 Years Old

Trending News Channel
Oct. 20 2014 6:17 PM Watch Flashes of Lightning Created in a Lab  
  News & Politics
Politics
Oct. 20 2014 8:14 PM You Should Be Optimistic About Ebola Don’t panic. Here are all the signs that the U.S. is containing the disease.
  Business
Moneybox
Oct. 20 2014 7:23 PM Chipotle’s Magical Burrito Empire Keeps Growing, Might Be Slowing
  Life
Outward
Oct. 20 2014 3:16 PM The Catholic Church Is Changing, and Celibate Gays Are Leading the Way
  Double X
The XX Factor
Oct. 20 2014 6:17 PM I Am 25. I Don't Work at Facebook. My Doctors Want Me to Freeze My Eggs.
  Slate Plus
Tv Club
Oct. 20 2014 7:15 AM The Slate Doctor Who Podcast: Episode 9 A spoiler-filled discussion of "Flatline."
  Arts
Brow Beat
Oct. 20 2014 9:13 PM The Smart, Talented, and Utterly Hilarious Leslie Jones Is SNL’s Newest Cast Member
  Technology
Technocracy
Oct. 20 2014 11:36 PM Forget Oculus Rift This $25 cardboard box turns your phone into an incredibly fun virtual-reality experience.
  Health & Science
Medical Examiner
Oct. 20 2014 11:46 AM Is Anybody Watching My Do-Gooding? The difference between being a hero and being an altruist.
  Sports
Sports Nut
Oct. 20 2014 5:09 PM Keepaway, on Three. Ready—Break! On his record-breaking touchdown pass, Peyton Manning couldn’t even leave the celebration to chance.