Counterintuitive Conclusion of the Day

Conclusion: Jack Layton and Stéphane Dion are effectively extreme right-wingers [1].

The proof is simple, based on two statements I hear a lot and which, based on their commonness, I have no choice but to assume are true without the need to question their validity.

1. All of the parties/party leaders are effectively the same. [2]
   
2. Stephen Harper is an extreme right-winger.

Because Jack Layton, Stéphane Dion, and Stephen Harper are party leaders, they are all effectively the same, by Statement 1. Thus, because Stephen Harper is an extreme right-winger by Statement 2, Jack Layton and Stéphane Dion are also effectively extreme right-wingers [3].

[1] By this I don't mean that Jack Layton and Stéphane Dion are effective at being extreme right-wingers. They are not (well, effectively, they are effective at being extreme right-wingers, as I suppose I have shown above). Rather I mean to say that it is difficult to distinguish one from the other.

[2] See footnote [1] above. Statement 1 has been put to me thus: All parties are evil. The only difference between them is the lies they tell to get elected.

[3] I'm well aware that we could apply the same argument to show that Harper and Dion are leftist moonbats or to show that Harper and Layton are probably not going to lead their respective parties into the next federal election. This effectively reduces the diversity of political persuasions, which are usually described as points on a line or occasionally a circle [3.1], to a point, thus rendering the terms "right-winger", "left-winger", and "centrist" effectively meaningless.

[3.1] It has frequently been acknowledged that a line is inadequate to describe the various political leanings. A circle has been proposed as an alternative. This too, I find inadequate, as a circle is merely a line with the ends connected. I prefer a plane, or perhaps some other 2- or higher- dimensional manifold. A non-orientable one would make things more interesting. But it is what it is, and we can't be choosy with reality now, can we? [3.1.1]

[3.1.1] Oops. I've gone and made the footnotes longer than the post again.

Post Election Thoughts

This past Wednesday, the province of Ontario held its latest provincial election. I didn't vote. If my memory serves me correctly, this is the first provincial election that I have not voted in since I've been eligible to vote. The party I would normally vote for doesn't seem to do well in this riding, and, besides, most of the campaign seemed to pass me by with out my noticing. I've been busy [1] and didn't have time to register in this riding (since it's not my home riding). All in all, it didn't seem worth my while to seek out a local polling station for them to tell me to go to another polling station where I would then find out that I lack sufficient documentation to prove my residency. Anyway. Enough with the excuses.

As usual we--and by we, I mean everyone but me--voted on who would form the next Government of Ontario. We also voted on whether to maintain the current first past the post (FPTP) system of representation, or to implement a new mixed member proportional (MMP) system of representation.

The Election

Aside from one issue, as far as I could tell, the election was mostly a matter of The Dud We Know vs. The Dud We Don't. Perhaps Archie comics have had a more profound effect on my life than they should have, but I don't think I could vote for a party led by a guy named Dalton. Even the new and improved Dalton seems to be at least 50% weenie. The main features of John Tory are that is first name is not Dalton, and that his last name is also the nickname of the party he leads.

I don't recall much that Dalton's done during these last four years. Somewhere along the line he did one or two things that I thought were good ideas at the time. I can't even remember what those were. He might even have broken one of his promises in order to do one of the things that I liked. For the most part, however, I didn't care enough to vote against him. John Tory didn't have much to offer me to get me out to vote for his party. I think he campaigned against Dalton's broken promises. As you may have guessed, that wouldn't be enough to entice me to vote for his party. There was the usual talk about tax cuts that we expect from the PC's, but nothing really inspiring. Then there was the issue of extending public funding to faith based schools. I doubt that this was part of any grand philosophy, nor that he meant it to be an election issue like it was. My guess--I feel it's more like stating the obvious than guessing--is that the leader was trying to win some votes from religious conservatives.

The spectre of religious groups receiving public funding certainly frightens a lot of people, myself included. As a religious person, the spectre of having my faith based organization funded by--and ultimately controlled by--the government certainly frightens me.

It was rather amusing to witness the reactions of the not-so-religious to the proposal here in Canada, where separation of church and state seems much more like something we fell into--if we really do have it at all--than a founding principle, and especially in Ontario, where a large number of students attend Catholic schools, which I presume, by their name, are based on some sort faith that I've heard about once or twice called Catholicism. Correct me if I'm wrong. If it is fear of funding fundamentalism, then the opponents need only take look at these schools. Hardly hotbeds of extremism. If they were to become so, the government would likely step in and stop them, as they've done before. If the Catholic schools are any example, then extending funding to all faith based schools is likely a better antidote to extremism than not. If it is the grand principle of separation of church and state that concerns them, then they should be agitating to withhold funding from Catholic schools just as passionately as they are to keep it withheld from other nonCatholic faith based schools. It doesn't seem like those who are arguing against it know what they're really arguing against. Nor does their position seem all that consistent.

Dalton disallowed all forms of religious arbitration, including Catholic, when Sharia courts were proposed a few years ago. He wasn't going to pick and choose which religious groups should be allowed arbitration, so he banned them all from doing it, even if they had already been doing it. If he is so opposed to other religious groups receiving public funds, why hasn't he taken the same position he did with religious funding as he did with religious arbitration? It's not like he hasn't taken a position on continued funding of Catholic schools. A quick google search will yield quotes from the man himself assuring the schools that they will continue to be publicly funded. So much for consistency. Sure there's the issue of the constitution. Damn the constitution, I say. This is important! Other provinces have gotten over this hurdle. I don't see why we can't.[2]

The Referendum

As I predicted, the No vote won. I'm surprised at how much it won by, however. I was expecting popular support for MMP to be at least 50%, but it didn't even make 40%. The number of ridings with more than 50% support was much smaller than I expected, too. Only 5 riding had more than 50% support for MMP.

Initially, I was opposed to any form of proportional representation (PR). There were primarily two parties who advocated it. These parties, of course, were the ones who had the most to gain if some form of PR was adopted. Much of their advocacy came across as thinly veiled self-interest, clothed in the rhetoric of fairness. Not only that but telling me "If Ontario had PR, then we would have more seats/at least one seat" was certainly not the way to advertise PR to me. I was happy with the number of seats those parties had, and wouldn't be upset if they had less. But to have more of them? I'll pass, thank you.

After hearing more about it from less self-interested parties, though, I warmed up to more. Not enough that I wanted it, but enough that I was disappointed that it didn't receive more support. If I could have voted "maybe", I'm might have been passionate enough about that option to have registered and gone out and voted.

There were a number of other objections that I raised to PR before I was told about any specific form of PR (there seem to be many). The MMP system seemed to take care of a lot of them. I wasn't crazy about the fact that there would be two types of MPP's. Don't ask me why, though. I don't know. Perhaps the hordes of objections to two tier health care that I've heard have instilled in me a latent dislike for two tiered anything, including MPP's.

I did like the possibility that I would be able to vote for the party and the local candidate separately. When I was back in Hamilton on Thanksgiving weekend, for example, I saw that there was candidate who I thought would be a good MPP, but who wasn't running for a party that I would normally support If we had MMP, I could have voted for him, but some other party. (Well, actually, I wouldn't have been able to vote for him, even I were voting in Hamilton. He was in the wrong riding.)

There are other things that MMP would have left unfixed, and might actually have made worse. For example, even under FPTP, MPP's are often elected with considerably less than 50% of the vote in their ridings. In that case, it is not so much that the MPP's are the best representatives, but rather they are the least-bad representatives. This is in part a function of the size of the ridings. Under the proposed MMP system, there would have been fewer ridings than now, so they would be larger, exacerbating the problem.

One of the strangest criticisms of the referendum that I've read in the wake of its outcome is that the material given out by the government was presented neutrally and without bias. How terrible that they would give me only the facts and let me think for myself and make up my own mind. Fascists the lot of them. Is it too late to vote out the bums? What? It is? Dammit!

I wonder why electoral reform has to go to referendum, as it just did in Ontario, and as it has previously in BC. What's to stop a (purportedly ill-gotten majority) government from simply legislating it. I wonder if McGuinty comes off as a hero to PR advocates for putting it to referendum, or if he comes off as a coward for doing so rather than just legislating it. If 60+% of the voters are happy with the system through which he obtained his ill-gotten majority, could that mean that it is not so ill-gotten? If the ill-gotten majority government did legislate some form of PR, would that new system be illegitimate because the government that legislated it had a majority of seats with less than 50% of the popular vote?

I've heard that some PR advocates are saying that MMP is the wrong form of PR to use. I wonder what they think is wrong with MMP and what they think would be better.

The issue of PR vs. FPTP reminds me of an example of a "paradox" in statistics that I heard about last year. There was an issue of whether Maori were represented adequately on juries in New Zealand. Statistics on Maori representation were presented in two different ways. In one presentation, only local statistics were given. In each jurisdiction, Maori's were underrepresented [3] on juries. In another presentation, only national statistics were given. In this case, Maori's were overrepresented [4]. Arguing that Maori's are underrepresented by the first presentation is analogous to choosing governments by FPTP. Arguing that Maori's are overrepresented based on the second is analogous to choosing governments by PR. It is not clear to me which statistics are relevant in determining whether the Maori are adequately represented on juries. Assuming that the analogy is legitimate, is it any clearer whether we should choose FPTP or PR?

[1] Read "lazy". But really. I didn't even use what spare time I had to do stuff for myself, such as grocery shopping. I'm so lazy, in fact, that I'm not going to bother hyperlinking my footnotes today.

[2] I once read that Ontario Catholics (and not Catholics in other provinces) have a strong tendency to support the Liberal Party. I wish I had a reference. I don't remember if this support was for the federal party, the provincial party, or both. If this support holds for the provincial party, then I doubt that the Liberals will be advocating this solution the the funding issue any time soon. I could get into conspiracies about McGuinty's own Catholicism, but I won't. Surely it's a coincidence. Surely.

[3] Under suitable definition of underrepresented.

[4] Under suitable definition of overrepresented.

Google Democracy

I wrote a post on this topic some time ago, but then decided to abandon it. However, a few days ago I received a brochure from some branch of the Ontario Government regarding the upcoming referendum on whether to replace the current First Past the Post system of representation with the Mixed Member Proportional system. In light of that, I decided to rewrite the post.

About a year and a half ago, I did a presentation in a math seminar on the PageRank algorithm that Google uses to rank pages on the web. They came up with a clever, though simple, idea to rank websites based on links between pages which greatly improved the quality of searches over search engines that predate Google. The algorithm is also resistant to abuse (though not completely abuse proof).

When I was researching the presentation, one of the things I read from Google itself was that it "relies on the uniquely democratic nature of the web". My first instinct when reading that is to groan. Thinking about it a little more, I realized that Google's algorithm really doesn't much resemble any democratic system that I've ever heard of. Later on, I asked myself what if? What if a country were to adopt a system modelled after the PageRank algorithm? How would/could that work?

The main idea behind Google's algorithm is the assumption that a link from webpage A to webpage B means that the author of page A thinks page B is good (of course, the author of A might link to B because of how bad B is, but, to imitateChandler Bing, perhaps the author of A thinks B is a good bad-website.) The term often used is authority. Thus, by linking to B, the author of A confers authority on B. The authority of web page B is then calculated based on the number of links pointing to B from some other website, but in a recursive way, which I'll try to explain now. Using the recursion, their algorithm calculates a score for each page as follows.

1. Give each page a score of 1.
   
2. For each page A, add up the points of the pages that link to A to get a new number. (This will be the number of pages that link to A).
   
3. Replace A's score by this new number.
   
4. For each page A, add up the points of the pages that link to A to get another new number
   
5. Replace A's score by this new number.
   
6. Go back to step 4.
   

At each step, each page gets assigned a new number. The numbers are going to get very large, so at each step they are also "normalized". That is, the numbers are all divided by one number to keep things from getting too large. (The number chosen may differ at each step). This is okay since it is the ranking of scores that is most important, and not so much the score itself, since we want to know the which websites are better than others, and not necessarily how good each site is. The process is repeated until the scores do not differ too much from one step to the next, so that each page has a ``final'' score.

There are a few other steps that are taken to prevent undesirable things from happening. For example if one page has a large number of links to other pages, then that page could have a strong influence on the algorithm and thus the overall ranking, so the "strengths" of links are scaled so that each page (or the author of each page) has the same amount of influence. For example, if there are 10 links from site A, then each of those links counts as one tenth of a link. If there are 2 links from site A, then each of those links counts as a half of a link. If there are n links from site A, then each of those links counts as one n-th of a link.

So why does this work? A rough measure of the authority of a page is the number of other pages that link to it. This is the score after the Step 3. Two pages, call them page A and page B, could have the same number of pages linking to them. At first we might think that the authority of A and B is the same. However, we could look at the pages that link to each of these, and count the total of the number of links into each of those pages instead. That is, we are counting the number of links to pages that link to each of A and B. These will be the new scores for A and B after we do Step 5 the first time (I'm fudging a little bit here). If there are many links to pages that link to A, while there are few links to pages that link to B, then intuitively, we feel A is better than B. So Even though A and B receive the same number of links, A is linked to by sites with more authority than those that link to B. We could go one step further back and count the numbers of sites that link to sites that link to sites that link to A and B and compare them (same fudge as before, but more of it). These numbers are the scores after we do Step 5 the second time. At each stage, the scores of A and B are updated in terms of the scores of the pages that link to them, so that the authorities of A and B are reinforced by the authority of the pages linking to them. A website that is linked to by many sites with a high authority score at each step will end up with a high authority score in the next step. Repeated enough times, the scores stabilize. That is, the scores don't change much from one step to the next. I illustrated this using two sites with the same number of links in, but it is possible that A could have a small number of links in, while B has a large number, but A's authority is higher than B after the process is repeated enough times.

So how would we use Google's idea to decide our elections? Suppose that we were to allow eligible voters to defer all or a portion of their voting rights to someone else. In such a system, I could retain all of my voting rights if I wanted. Otherwise I can defer my voting rights to someone else. In the language of the internet, I have linked to that person. Linking to that person implies voting authority. In the case that I retain my vote, I link back to myself. In between these two extremes, I could retain retain a portion of my voting rights, one half, while deferring the other half of my vote to you. I have linked to myself with a link of weight 1/2 and linked to you also with a link of weight 1/2. Perhaps I could split the remaining half of my vote between you and someone else, so that there is a link to myself with weight 1/2, and a links from me to you and someone else, each of weight 1/4. Otherwise, I could split my voting rights between the three of us evenly, or.... I could divide my vote any number of ways between any number of people, so long as the portions of my vote that I've given to everyone else adds up to 1, in line with the principle of "one person, one vote".

Then a "vote-authority" score would be calculated by a process similar to that described above. The process will be slightly different, because the "weigths" of the links from me to each person can be different, but I won't get into that here. The vote-authority score of person A is reinforced by the vote-authority score of the people that defer a portion of their voting rights to A. On election day, the weight of each persons vote is their vote-authority score. Instead of adding up the number of votes that a candidate gets, the scores of the people that voted for that candidate are added up. Whichever candidate has the highest score wins the riding (or whatever is at stake in the election), rather than the candidate with the largest number of votes.

You might ask why I would want to defer my voting rights to anyone at all besides myself. On election day, I am required to choose one of the candidates in my local riding who I think would best represent the constituents that riding in the legislature, which of course is the one that best represents my own political preferences. Usually, I don't know much about the candidates (though some are easy write-offs). Finding out is a lot of work, and what information I do find may not be reliable. Somebody else might know the candidates better than I do, or else they might know somebody who does. In the first case, they can make a more informed decision than I can. In the second case, they can choose to defer their judgement to a person who knows more about the candidates. Perhaps I just trust that person's judgement on political matters more than I trust my own. Perhaps I'm just lazy, and I want you to vote for me.

The idea that one person's vote could be worth more than another on election day is probably offensive to some. Those people shouldn't get too worked up. I'm not seriously proposing that we implement such a system, or any variation of it (it would probably be hard to implement). I am, however, curious to see how different things would turn out if such a system were implemented. Would the election results be more or less the same as they've always been? Would one party end up dominating? Would the major parties parties receive a larger or smaller share of the "popular vote" than they do now? Even if I were serious, however, I don't think that there would be that much to object to. We would each get one vote. The main difference is that how we use that one vote. Instead of using that one vote to decide on politicians, we use it to decide on who is qualified to decide on politicians. One of the claimed benefits of proportional representation is that it would increase participation in elections. If my crazy system is implemented, people can exercise their right merely by deferring all of their voting rights to someone else, and then staying home at night enjoying the election coverage on tv. How could the privilege to vote without leaving the comfort of your armchair nothing fail to increase participation?

If you think this idea is dumb, by the way, blame it on Google. They're the ones who connected the notion of hyperlinks to democracy in the first place. If you think it's a good idea, however, I expect full credit.

Since the referendum is on MMP, you might be wondering what my thoughts are on that. I think it probably won't pass, since, in order for to pass, it must receive the support of 60% of the population, as well as 50% of the vote in at least 60% of the ridings. Those seem like pretty strict conditions to me. So who cares.

I have my own idea for a system of proportional representation. See, a lot of people criticize the first-past-the-post system on the basis that voters are misrepresented, especially those in less popular parties, since the percentage of province wide (or nation wide) vote share does not translate into the same percentage of seats. MMP would still have 90 of the MPPs chosen by the first-past-the-post system to represent ridings. Of course, as is often the case now, someone could get elected to a riding with less than 50% of the vote in that riding. That means that more than half of the people there are misrepresented. This is simply unfair. In fact, it would be unfair even if the winner received more than 50% of the vote in that riding, since those who voted for other parties get no local representation by their preferred party. Second place candidates often get support in the 20-30% range, and sometimes even higher. If it's unfair that roughly 10% of the population votes Green, yet the party receives no representation, then it is most certainly unfair that an even higher percentage of voters in a riding receives no local representation by their preferred party. Since each voter in a riding should be fairly represented in the legislature, I propose that each candidate be appointed as the MPP of the riding for a time proportional to the vote share. Thus if a candidate gets 40% of the vote, then they are appointed MPP for 40% of the term. The candidate with the highest percentage would go first, followed be the next highest, and so on, until the end of the term. (Thank you McGuinty for fixed election dates, without which this entirely rational scheme could not be implemented.) This would solve both province wide and local discrepancies between voter preference and representation. It would also take care of the fact that we get tired of hearing the same politicians talking for four years straight. Queen's park would be a mad house by the end of the four years, what with the Libertarians picking fights with both Marxist-Leninists and Communists, while latter two parties fight vehemently with each other over policies that are indistinguishable to any unenlightened onlookers. But I'm willing to pay that price for the sake of fairness. What about you?

You're only supposed to do that on a bike!

Last night, a somewhat unusual thing happened while I was walking home. I was crossing an intersection with the light (which is unusual for Kingston pedestrian traffic). As I was crossing, a car pulled into the intersection "against" the light. The light was red for her, and she was stopped for a moment before she pulled into the intersection. I slowed my pace, hoping the presence of a pedestrian in her path would make her realize that it wasn't her turn to go yet. It didn't. She looked at me like I was confused, and once I had gotten out of her way, she just kept on going. Right now, you're probably thinking, "Randy, when the lights are flashing on the police car, you're supposed to wait for it to go." There were too many rust spots, and not enough flashing lights for this to be a police car. Also, there were too many crazy looking old ladies driving.

I've almost done it a few times myself in the past, though. But I have never even gone far enough into the intersection to get in the way of pedestrians trying to use the crosswalk (in one of those rare Kingston moments when someone can't get through the intersection before the light turns green). Usually when it happened it was when I'd been biking a lot. When I'm on my bike, as with walking, I don't often bother waiting for the light to turn green. I just wait until the cars have cleared. When I would get in my car, my cycling instincts would still be in play. The worst that happened was when I was making a left hand turn one time, and almost cut off a cyclist who was going straight. I did wait for the light to turn green though. So did the cyclist, and it was almost his downfall.

Linking Mathy Thoughts

What must be the most unusual reason for struggling with math that I've ever heard. Hat tip to Cosh.

What may or may not be a joke. Hat tip to the Blogless Erica.

What may replace trigonometry some day. Hat tip to myself.