# lionhearted comments on Of arguments and wagers

• Mul­ti­ple fas­ci­nat­ing ideas here. Two thoughts:

1. Solo for­mu­la­tion → open to mar­ket mechanism?

Jump­ing to your point on Re­cur­sion — I imag­ine you could ask par­ti­ci­pants to (1) spec­ify their premises, (2) spec­ify their ev­i­dence for each premise, (3) put con­fi­dence num­bers on given facts, and (4) put some­thing like a “strength of causal­ity” or “strength of in­fer­ence” on causal mechanisms, which col­lec­tively would out­put their cer­tainty.

In this case, you wouldn’t need to have two peo­ple who want to wa­ger against each other, but rather any­one with a differ­ence in con­fi­dence of a given fact or the (ad­mit­tedly vague) “strength of causal­ity” for how much a true-but-not-the-only-vari­able in­put effects a sys­tem.

Some­thing along these lines might let you use the mechanism more as a mar­ket than an ar­biter.

2. Dis­count rate?

After that, I imag­ine most peo­ple would want some dis­count rate to par­ti­ci­pate in this — I’m try­ing to figure out what odds I’d ac­cept if I was 99% sure in a propo­si­tion to wa­ger against some­one… I don’t think I’d lay 80:1 odds, even though it’s in the­ory a good bet, just be­cause the sole fact that some­one was will­ing to bet against me at such odds would be ev­i­dence I might well be wrong!

The like­li­hood that any­one par­ti­ci­pat­ing in a thought­ful pro­cess along these lines and lay­ing real money (or other valuable com­mod­ity like com­put­ing power) against me means there’s prob­a­bly a greater than 1 in 50 chance I made an er­ror some­where.

Of course, if the time for Alice and Bob to pre­pare ar­gu­ments was suffi­ciently low, if the re­source pool Kelly Cri­te­rion style was suffi­ciently large, and there was suffi­cient liquidity to get re­gres­sion to the mean on rea­son­able timeframes to re­duce var­i­ance, then you’d be happy to play with small dis­counts if you were more-right-than-not and rea­son­ably well-cal­ibrated.

Any­way — this is fas­ci­nat­ing, lots of ideas here. Salut.