| repak shawahb | |||||
| your little sister's cesspool tea party | |||||
blogroll |
Sat, 08 Jul 2006 Mike, Katie (Dominus), Cyrus, and I were grabbing a bite at T.G.I. Friday's last night and talking about Al Gore appearing on the Daily Show and claiming (tongue-in-cheek, at least to an extent) that he really did win Florida. This jump-started us on a discussion of the issue, and opinions flew: Gore really did win it, we fucked up, this, that, whatever. I take exception to such claims, not because I'm a fan of Bush (at this point it must be admitted that the country has taken a turn for the worse under his presidency, and no I'm not turning into some pinko commie liberal weenie), but because the reality of the matter is one that our electoral system is not designed to handle, namely, the result was so close that it was literally undecidable. The 190-odd votes one way or the other were below the noise floor. In other words, because of the particulars of the way votes are taken and counted, the election cannot be resolved with enough precision to give a number to each candidate which is more accurate than, say, plus or minus a thousand votes. The election in Florida was metastable, and the Supreme Court ended up acting as the bounded-time arbiter. Having stated the matter this way, I realized something else: the electoral college makes this problem much worse. Here's how: the noise level in the system is more or less independent of the number of participants, since it arises largely from very local phenomena (i.e., it is generated in each voting precinct, and the number of people per precinct is approximately constant). The signal, on the other hand, scales directly with the number of people participating in a given election. Because of the electoral college system, however, the apparent number of people voting is artificially limited, since each of the states happens as an independent voting event (and thus we really have 50 small elections, not one large one). Thus, assuming that we had 50 equally-sized states (we'll come back and deal with this in a second), we have 50x less signal versus the same noise, i.e., an apparent 34 dB rise in the noise floor per election event due to the electoral college. Now, when you average all of these back together, you should get exactly a 34 dB fall in the noise floor, right? Wrong. The problem is this: because of the way electors are assigned (one per Senator or Congressman), the SNR cannot be recovered completely: small states are actually overrepresented in the electoral college (because Representatives are a function of population, but Senators are a constant for every state, and in small states the Senators represent the majority of the electoral clout), and it is in these very states that the SNR is worst. Thus, we end up averaging a set of results which has been distorted in a way that cannot fail to increase the noise—the results which get greater marginal weight are exactly the ones where the SNR is worst. So what is this added noise, really? It's distortion and quantization noise! Instead of keeping everything high resolution (i.e., in terms of actual votes), we quantize on artificial boundaries and then make the final decision on a set of discrete values which are not only low-rez, but skewed. What, then, does this suggest about fixing the electoral college? Clearly, one way to fix it is to get rid of it. But it's worthwhile to imagine instead what would happen if we had a thousand states instead of fifty: we'd be making a final decision based on bits which, while they each hide a greater quantity of "thermal" noise (due to imprecisions at the precinct level, et cetera), contribute less quantization noise to the final outcome. At this point, the quantization portion of the noise goes away, and we're left only with the problem of distortion. So really, to fix the electoral system, we need each elector to represent precisely the same number of voters, and for the number of electors to be enormous. Isn't a popular vote just better? Side note: what if instead of electing based on a single event, we oversampled the voting population? Say, everyone votes in 16 elections, and we actually feed back the results from the previous election, in effect shaping the quantization noise from the decision while simultaneously attenuating (by way of the gain in the feedback loop) the noise contribution of the election process itself. Seems like overkill, but holy shit it would be cool if our electoral system were more like a delta-sigma data converter. [ permalink | 5 comments ] writebacksjdoege wrote No. repak wrote how exactly is it jdoege wrote Here's how... repak wrote thank you jdoege wrote Politics is fun. post a comment: |
||||