[extropy-chat] three coins in a fountain, part 3: the test

[Chris Hibbert]

Hal wrote:
> I looked a bit at the mathematics of a slightly different form of the
> puzzle and got a (possibly) surprising result.

Economists (and I don't know who else) are quite interested in eliciting 
people's best estimates.  It turns out that if you use what's called a 
log-based scoring rule, the respondents' best strategy is to give their 
best likelihood estimate.  The way spike  formed his scoring rule leads 
to the results Hal talked about.

 From one of Robin's papers (http://hanson.gmu.edu/combobet.pdf):

          s[i] = a[i] + b log(r[i]
    The logarithmic rule is the only rule that can be used both to
    reward an agent and to evaluate his performance according to
    standard statistical likelihood methods.  Scoring rules have
    long been used in weather forecasting, economic forecasting,
    student test scoring, economics experiments, risk analysis,
    and the engineering of intelligent computer systems.

The resulting scores on individual test items are added together, rather 
than being multiplied to get a total score.

Robin has another paper "Logarithmic Market Scoring Rules for Modular 
Combinatorial Information Aggregation" that talks about other ways of 
using the Logarithmic rule.

I expect Robin will weigh in shortly to correct me.

Chris
-- 
C. J. Cherryh, "Invader", on why we visit very old buildings:
       "A sense of age, of profound truths.  Respect for something
       hands made, that's stood through storms and wars and time.
       It persuades us that things we do may last and matter."

Chris Hibbert
hibbert at mydruthers.com
Blog:   http://pancrit.org