Jul. 12th, 2006
St. Petersburg paradox
Jul. 12th, 2006 01:07 pmImagine a game in which you:
* win $2 with probability 1/2
* win $4 with probability 1/4
* win $8 with probability 1/8
* win $16 with probability 1/16
* win $32 with probability 1/32
and so on, ad infinitum.
Assume also that your payoff will be determined and paid up instantly.
How much would you pay to play this game?
The expected value of the game is
St. Petersburg paradox
And I think this behavior is perfectly rational.
Your answer to the question above is a measure of your risk-aversity. But we should also investigate the effects of a lower-payoff vs a higher payoff game.
A game paying twice as much as the above game:
* win $4 with probability 1/2
* win $8 with probability 1/4
* ...
is obviously a better game to play (almost twice as good), and yet, the expected value of the game is also infinity.
My solution would be to make a transformation on the probabilities that makes the sum converge. The idea is that we have a "horizon", and very remote probabilities should count for less. But a 1/8 probability should count almost the same as a 1/2 probability. Any concrete solutions?
One problem is that you can always make a game with payoffs that make this sum diverge: just make the payoffs proportional to 1/p. This is not too problematic however: IMHO, the real problem is unbounded utility. Founding utility on human happiness is a good way out (I think).
* win $2 with probability 1/2
* win $4 with probability 1/4
* win $8 with probability 1/8
* win $16 with probability 1/16
* win $32 with probability 1/32
and so on, ad infinitum.
Assume also that your payoff will be determined and paid up instantly.
How much would you pay to play this game?
The expected value of the game is
1/2 * 2 + 1/4 * 4 + 1/8 * 8 + ... =
1 + 1 + 1 + ... = infinitySt. Petersburg paradox
A naive decision theory using only this expected value would therefore suggest that any fee, no matter how high, would be worth paying for this opportunity. In practice, no reasonable person would pay more than a few dollars to enter. This seemingly paradoxical difference led to the name St. Petersburg paradox. [huh? why this name? -GL]
And I think this behavior is perfectly rational.
Your answer to the question above is a measure of your risk-aversity. But we should also investigate the effects of a lower-payoff vs a higher payoff game.
A game paying twice as much as the above game:
* win $4 with probability 1/2
* win $8 with probability 1/4
* ...
is obviously a better game to play (almost twice as good), and yet, the expected value of the game is also infinity.
My solution would be to make a transformation on the probabilities that makes the sum converge. The idea is that we have a "horizon", and very remote probabilities should count for less. But a 1/8 probability should count almost the same as a 1/2 probability. Any concrete solutions?
One problem is that you can always make a game with payoffs that make this sum diverge: just make the payoffs proportional to 1/p. This is not too problematic however: IMHO, the real problem is unbounded utility. Founding utility on human happiness is a good way out (I think).
access rights in MediaWiki
Jul. 12th, 2006 02:23 pmAccording to this:
I would have to whitelist all pages, except for the few private ones. It would be much easier to blacklist them, especially if I could do it by having something like
Another solution is to make another wiki for private stuff, and link them through interwiki.
# Pages anonymous (not-logged-in) users may see
$wgWhitelistRead = array ("Main Page", "Special:Userlogin", "Wikipedia:Help");,I would have to whitelist all pages, except for the few private ones. It would be much easier to blacklist them, especially if I could do it by having something like
{{read_access=authorized_group; edit_access=authorized_editors}} at the top of the page.Another solution is to make another wiki for private stuff, and link them through interwiki.
Brazilian politics
Jul. 12th, 2006 06:36 pmPity the Brazilian Voter is a very good summary of Brazilian politics. Main points:
* most parties have no ideologies, as can be seen by the alliances
* no party is very concerned about lowering taxes
In my opinion, the most serious problems in Brazil are:
* starting a business is very hard because interest rates are ridiculous. If banking were deregulated, private bankers could make lots of money. (Btw, do credit givers anywhere ever make personalized investigations, in order to assess someone's credit-worthiness? I think anti-discrimination laws tend to get in the way of this.)
* taxes are way too complex.
* Corruption exists at all levels, and is accepted as part of the culture. Meritocracy is far behind Friendocracy.
By the way, Brazilian government bonds are probably a good investment.
---
I also like this piece: World Cup brings Out the Best and Worst in Brazil.
* most parties have no ideologies, as can be seen by the alliances
* no party is very concerned about lowering taxes
In my opinion, the most serious problems in Brazil are:
* starting a business is very hard because interest rates are ridiculous. If banking were deregulated, private bankers could make lots of money. (Btw, do credit givers anywhere ever make personalized investigations, in order to assess someone's credit-worthiness? I think anti-discrimination laws tend to get in the way of this.)
* taxes are way too complex.
* Corruption exists at all levels, and is accepted as part of the culture. Meritocracy is far behind Friendocracy.
By the way, Brazilian government bonds are probably a good investment.
---
I also like this piece: World Cup brings Out the Best and Worst in Brazil.
SENS Challenge: the verdict !
Jul. 12th, 2006 08:19 pmNobody has won the $20,000 SENS Challenge!
Technology Review's article:
P.S. Amazingly, it seems I beat
crasch and
tdj to the punch this time.
Technology Review's article:
Last year, Technology Review announced a $20,000 prize for any molecular biologist who could demonstrate that biogerontologist Aubrey de Grey's "Strategies for Engineered Negligible Senescence" (SENS) -- a much publicized prescription for defeating aging -- was "so wrong that it was unworthy of learned debate."
P.S. Amazingly, it seems I beat
GusWiki: anonymous edits are disabled
Jul. 12th, 2006 09:49 pmGusWiki got spammed twice already today.
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