Are all bets off when it comes to agreement gambles?

Abstract

It is well known that views on social issues are influenced by demographics. Whether similar people agree or dissimilar people disagree on touchy topics are useful insights that social science articles point to. These insights remain “internal” to the system, so to speak. In this work, using data from a Bentley–Gallup survey and the martingale mathematics of e-values, we showcase how someone “external” to the system could exploit these insights to build up a huge fortune. We achieve this through two parts. First, by showing the internal predictability will help (that is, if, for instance, similar people agree, that it is useful knowledge, as is if similar people predictably disagree). Second, by analyzing the aggressiveness or conservativeness of the “external” better (how much of the current wealth should they bet on the next issue/question) which has got nothing to do with whether similar people agree, that is, with the previous part. We recommend certain optimal ways to bet, with and without demographic knowledge of the participants.