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That is not strategy proof
Oh, I see. You probably already understood that, but I'll write it up for anyone else who didn't initially grok the process (like me).
Intuitively, the original algorithm incentivises people to post their true estimates by scaling up the opponents investment with your given odds, so that it doesnt pay for you to artificially lower your estimate. The possible wins will be much lower; disproportionately to your investment, if you underestimate your odds. Conversely, the possible losses will not be covered by increased wins if you overestimate your chances.
It does not work if you scale the bets. If A believes he wins the bet half the time, and B believes it will be 90%, with the assumption of B being honest and both players setting the limit at 1 (for ease of calculation):
With A declaring 50%, the investment ratios would be:
A: 0.24
B: 0.56
With the original amount calculation that gives the expected value of
E(A) = (0.5 * 0.56 - 0.5 * 24) = 0.16
Whereas with scaled up bets A puts in 0.43 while B gives 1:
E'(A) = (0.5 * 1 - 0.5 * 0.43) = 0.285
With A declaring 20%, the numbers are:
A: 0.03
B: 0.17
E(A) = 0.5 * (0.17 - 0.03) = 0.07
While with scaled bets (B = 1, A = 0.18)
E'(A) = 0.5 * 1 - 0.5 * 0.18 = 0.41
Note how E(A) goes down if A lies, but E'(A) went way up.
In order to give the players incentives to be honest, the algorithm seems to "use up" some of the total potential profit. For example, in the OP, the players are instructed to bet $2.72 and $13.28 when each was actually willing to bet up to $25. I think this also means that this method of coming up with bet amounts is not strategy proof if players are able to lie about their maximum bet amounts.
What's wrong with just using this algorithm to establish ratios between bets, then scaling up to meet whichever limit is hit first?
In your example, it'd be scaled up to 5.12 against 25.
A: 60% confidence B: 30% confidence
- af = .6 **2 == .36
- bf = .3 **2 == .09
- A pays (af - bf) * 25 == $6.75
- B pays (bf - af) * 25 == -$6.75?!?!
My intent is to demonstrate that, while the above is probably incorrect,
You put in the square of probability you think you're correct minus the square of probability he thinks you are correct all times 25. He uses the same algorithm.
is not an adequate explanation to remember and get the right result out of, because the calculations I specified above are my genuine interpretation of your statements.
(this problem persists for every value of p and q, whether they total to above 1 or not)
Neither probability should be <50%, you take the probability that your opinion is the right one, not whether the proposition is true or false.
In your example B would be betting against his beliefs, thus the negative result.
The right calculation: A = 0.6 B = 0.7
A pays: (A ^ 2 - (1 - B) ^ 2) * 25 = (0.36 - 0.09) * 25 = 6.57
B pays: (B ^ 2 - (1 - A) ^ 2) * 25 = (0.49 - 0.16) * 25 = 8.25
Edit:
actually, it's sufficient that A and B sum to over 1. Since you can always negate the condition, the right calculation here is:
A = 0.4
B = 0.7
A pays: (A ^ 2 - (1 - B) ^ 2) * 25 = (0.16 - 0.09) * 25 = 1.75
B pays: (B ^ 2 - (1 - A) ^ 2) * 25 = (0.49 - 0.36) * 25 = 3.25
Also, apparently I can't use the retract button the way I wanted to use it.
You speak as if these two are the only people on the planet.
Well, it's none of anyone elses business, so I don't see how other people being there is relevant.
If you mean it in the sense of "don't settle for someone who isn't going to help you with kids, no matter how good a match you otherwise are"... Never settle is a brag
If the guy wants children but is unwilling to spend time, I think the woman should kick him in the balls several times. Just to be sure.
The guy doesn't want children, but he doesn't mind having children with the woman as long as it's not too bothersome for him. The woman either really wants children, in which case this arrangement is to her benefit, or does not want children that badly, in which case they don't have children.
The ambiguity is intentional, apparently.
Huh!
Now I'm even more confused. How can my answer be useful if they don't know how I interpret the question? Esp. since my answers are pretty much opposite depending on the interpretation...
My bad for not finding that comment. I skimmed through the thread, but didn't see it.
In response to
2013 Less Wrong Census/Survey
I'm confused by the CFAR questions, in particular the last four. Are they using you as 'the person filling out this survey' or the general you as in a person? "You can always change basic things about the kind of person you are" sounds like the general you. "You are a certain kind of person, and there's not much that can be done either way to really change that" sounds like the specific you.
Help?
Well, a pretty frequent alternative is complaining a lot and looking for sympathy. Another is blaming someone else.
I think if you would ask those people they would also say yes, that they are thinking about ways of solving their problems.
I think if you would ask those people they would also say yes, that they are thinking about ways of solving their problems.
Not necessarily. They might say it's too big to solve, or "it's not really a big deal" when it obviously is, or that it's not their responsibility to solve, or any of multum other excuses that validate not changing.
It is generally also a good idea to come and meet us at a Meetup.
That does sound like a good idea. Browsing the google groups, the next occasion seems to be the CZE outing on 1. Sep. (http://lesswrong.com/r/discussion/lw/ie0/meetup_comfort_zone_expansion_outing_london/).
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Grooveshark (http://grooveshark.com/)! Unless you cannot stomach songs playing out of order, or sometimes being repeated (and even that is getting more rare as they work on improving their indexing).
Open page, type artist name (or select genre), press 'play all'. It stops playing every couple hours (which I enjoy - means I can just put music on in the evening and it'll turn itself off eventually - no need to get up) so you'll have to press a single button to resume.