Concerning Danny Hillis' arguments on "How Democracy Works (Or Why Perfect Elections Should All End In Ties) " I'd like to point out that they are well known in political science. As a matter of fact, there is even a theorem (can you imagine, a theorem in political science?) that states it all rigorously. This so called median-voter theorem states that if two parties are trying to maximize their share of the votes, the only Nash equilibrium (each party making a best response to the other candidate's choice) is where both candidates chose the platform of the median voter's ideal policy.

While the assumptions underlying this theorem, originally proved by Hotelling in the context of consumer preferences in 1929, are rather stark — but not different from Danny's example — (it is assumed that voters have single-peaked preferences over a left to right one-dimensional issue space, and that everyone turns out and votes for the candidate whose platform they prefer), it turns out that the theorem's conclusion is robust in many respects. That is, modest departures from most of the canonical assumptions lead to only small changes in the candidates' behavior.

The present presidential platforms, while far from fitting the classical assumptions exactly, seem to indicate that the median voter theorem applies to even more general cases.

In the digital universe, every bit makes a difference. In a democracy, every vote counts. Punched card ballots are where these two universes coincide. On November 4, 1997, in Ferndale, Washington, the difference between two candidates for city council came down to one bit of difference on one card.

"There's not much case law on this," argues Frank J. Chmelik. "The responsibility of the canvassing board is to certify that universe of ballots that make up the count. A recount is to re-count the ballots. It doesn't make any sense to expand the universe of ballots. It would frustrate the purpose of the law to allow the recounting of an infinite set of ballots. It may have been in a sealed envelope but it was in a white envelope, not a pink envelope." It is December 19, 1997 and I am in Whatcom County Superior Court, listening to arguments before Judge Michael Moynihan in the matter of Yvonne Goldsmith vs. the Whatcom County Canvassing Board. Yvonne Goldsmith came in one vote ahead of Lloyd Zimmerman in the race for Ferndale City Council on election night. After a mandatory manual recount and the discovery of a lost ballot, she is now one vote behind. Her lawyers have appealed for a second recount, this time by machine. Said machine to be a Documation card reader, one of the models now built by Cardamation of Phoenixville, Pennsylvania — if the appeal is upheld. Right now the lawyers are arguing over whether to include an absentee ballot — discovered in a sealed envelope at the time of the first recount — whose validity depends in part on whether the envelope it turned up in was white or pink.

"It doesn't make any sense for a subsequent computer recount to supersede the manual recount," argues Karen Frakes on behalf of Whatcom County Auditor Sheila Forslof, returning to the issue of human beings vs. machines. "We have no reason to believe the computer recount will be any different."

Chmelik, however, cites chapter and verse of a statute (RCW 29.64.010) which "allows for second recount upon application by the candidate, who may specify such recount be done manually or by (electronic) vote tally machine. Goldsmith has a right to an electronic recount that will control."

Judge Moynihan, who is reading the fine print, refers to a clause (RCW 29.62.050) which "stipulates `a recount by machine shall use separate and distinct programming.' Can you explain?" Chmelik explains how the vote counting software will be freshly installed (under Windows 95) from a copy delivered from the State Capitol under official seal.

After some deliberation the judge decides: "They have to count that ballot. As to whether or not the candidate is entitled to an electronic or manual recount — she's entitled to make that choice. If there's a discrepancy, well, it will probably have to be decided by another court."

The recount (by machine) is scheduled for Tuesday, December 23, at 9:00 a.m. I arrive at the Whatcom County Courthouse at the appointed time and am ceremoniously signed into the room. No one, as far as I can tell, has ever heard of Wired magazine. The Bellingham Herald, a few blocks away, hasn't bothered to send a reporter but is awaiting the results by phone. The card reader sits facing the end of a long boardroom table, with various officials arrayed on either side. The reader is hooked up to an IBM 300GL PC, with the "separate and distinct programming" occupying an external Iomega Zip Drive. The software, produced by Computer Elections of Benicia, CA, is up and running under Windows 95.

Pete Griffin, elections supervisor, is fiddling with the card reader. He's proud of how much the machine cost and that it's recently been factory rebuilt. A number of minor dignitaries are present, as well as representatives for the two candidates and two official scrutineers. Lots of sealing and unsealing of metal boxes containing the ballots, with forms signed and witnessed in triplicate every time a deck of punched cards makes a move. The card reader is fired up. It runs through a series of "Logic and Accuracy" test decks from the Secretary of State. The results are compared with the results from election night, when the Logic and Accuracy decks were placed under the seals we just removed. It's a cryptic process, and we all just take the word of Peter Griffin that the string of characters generated on the monitor means everything's OK. The reader flutters smoothly through the piles of cards without missing a single beat — far smoother than the readers I saw at Cardamation, being tested against cards that had been stored for many years.

Finally, it's time to count the ballots. It doesn't take long, a few minutes at most. We all hold our breath. The manual recount was repeated three times, under strict supervision, and all three counts showed Zimmerman one vote ahead. Is this the moment of truth? I'm watching the floor under the machine, to see how many bits of "chad" — the card stock that is punched out to make a hole — fall out when running through the decks. Occasionally, in running through the vacuum-fed reader at high speed, a bit will be dislodged from a ballot. This is a problem with partially pre perforated ballots — and human beings who sometimes start to punch out one location and then change their mind. As Larry Olsen, the Republican observer, whispers to me when he senses what I'm thinking, "If chad falls out there's no way to put it back."

I count nine bits of chad on the carpet after all the ballots are run. The chad may just have fallen innocently out of the innards of the machine, it may have fallen out of any number of punch positions which had nothing to do with the city council race, or one or more bits might have fallen out of the Zimmerman-Goldsmith positions. Who knows? The seconds tick by, and I am acutely conscious at this instant that language and reality sometimes coincide: in the punched card universe a "bit" really is a bit, and Gregory Bateson's definition of information as "any difference that makes a difference" is true indeed, as we await the count of how many bits of difference between card and not-card have just passed through the Cardamation machine. Pete Griffin sits down at the PC, enters some commands, navigates through some dialog boxes, and a Hewlett-Packard laser printer begins to hum. It's a tie: 954 to 954. The statistics show one "overvote" — a ballot where both candidates have received a vote. Someone asks Goldsmith's representative if she would like to run the cards again. No.

The auditor consults the Laws of the State of Washington and announces that the election will now be decided by flipping a coin. The candidate who filed first — Goldsmith — gets to call it heads or tails. Three days later, Judge Moynihan tosses a 1921 silver dollar in the air. Goldsmith calls it tails — and wins. Goldsmith gets the seat on City Council, while the Judge awards Zimmerman the coin. The "Logic and Accuracy" decks go back, under seal, to the Secretary of State. We live in a binary universe — and what isn't governed by logic is governed by chance.

Response to Luyen Chou

Luyen Chou is correct is pointing out that the model I used to explain ties is very much simpler that reality. However, I do not believe that the factors he describes interfere with feedback mechanisms described in the essay. It is certainly true that voter preference is determined by many factors, and that many of these factors are not under control of the candidates. This means that the candidate must use the variables that are under their control to achieve electablilty. If the candidates have many such issues to choose from, they may very well adopt different stances on particular issues to achieve the same net effect. Thus, both candidates may be in the optimally electable position in spite of holding very different positions on a particular issue, and spite of other voter preference factors that are beyond their control.

Danny's argument for the statistical merits of two-party democracy seems to me to be completely sound when considered in an idealized political setting. But it ignores the reality of the contemporary American political landscape in which elections are invariably decided by much less rational considerations than Danny's article would have one believe.

To be more specific, the argument relies on a fundamentally unrealistic assumption: namely, that voters vote based on an analysis of the candidates' positions with respect to specific, definable issues — and the proximity of these positions to their own.

In fact, one has only to read the opinion polls or listen to interviews with voters to know that, overwhelmingly, voters cite much more qualitative reasons for choosing one candidate over another. So, Gore is "arrogant", "overbearing", "smart", or "well-informed"; Bush is "inexperienced", "immature", "compassionate", or "good-natured" (these were adjectives used to describe the candidates in actual interviews with voters conducted byThe New York Times during the course of the election). In fact, it is probably safe to say that a large percentage of voters aren't even aware of what the candidates' positions are on the issues. Of course, one cannot simply blame an uninformed electorate for this phemonemon. In many cases, the candidates purposely obfuscate their position on popular issues to improve their chances of getting elected. For instance, during the final 2000 presidential debate in East Lansing, Michigan, George W. Bush refused to say that he was against affirmative action, despite repeated questioning, choosing instead to say that he was for "affirmative access" — whatever that means. And then there is the fondness among politicians for stating their position on issues at such a level of abstraction as to become virtually meaningless. Hence, we have Republicans who claim to be "pro-family values", which leads one to the absurd conclusion that Democrats are "anti-family values". Conversely Democrats often claim to be "pro-environment" as if to say that Republicans are categorically "anti-environment".

Danny's argument would also have you believe that the ideal candidate should conduct polls on every important political issue, and simply adopt the more popular position. But, as we all know, campaigns aren't run this way. One reason for this is the fact that being perceived as wishy-washy and unprincipled may be more damaging to the candidate than supporting the "wrong" side of an issue. In other words, candidates are widely perceived to be more than the sum of their positions. Instead, we look to them to be principled leaders and steadfast in their convictions.

Two other reasons for candidates to ignore the polls are the influence of special interest groups in election politics, and in the case of presidential politics, the quirky nature of our (now infamous) electoral college system. While the majority of Americans clearly support tighter gun control laws, Al Gore rarely mentioned his support for such laws on the stump. Why? Because he knew the importance of winning the swing votes of Rust-Belt (Reagan) Democrats, many of whom happen to be gun owners. In the case of special interests, candidates are forced to downplay or obfuscate their true positions on issues (positions that may be supported by the majority of the electorate) because of the political influence that these special interests wield (again, one has to look no further than the NRA to find an organization that can be, at once, so out of touch with America's electoral majority, yet strike such fear in the hearts of politicians).

I think American Democracy is both better and worse than the idealized description Danny provides. On the one hand, I am, like many others, often dismayed by the influence of special interests in American electoral politics; I am frustrated by the sometimes superficial and haphazard manner in which the American electorate comparison shops for candidates; and I am frankly puzzled by the need to maintain our seemingly antiquated electoral college system. But I am also moved by the humanity of the American electoral process. Americans bring all sorts of rationales with them to the polls -- some sound, some misinformed. But on one day in November, they have an opportunity to pull a switch one way or the other, and God help those who try to predict the outcome. If this weren't the case, we might as well let one of Danny's supercomputers do the voting for us.