In the first two articles of this series, we saw some broad trends in juror voting patterns and then we took a closer look at cases in which attackers attempted to bribe jurors. In this article, we will consider a number of other interesting questions and observations that have arisen regarding the behavior of jurors in the Doges on Trial pilot.The “lazy strategy” of always voting for the most common response
In the first article in our series, we saw that roughly 70% of all votes cast were for “not doge.” Then, one might naturally ask if it is/would have been profitable to set up a bot that deposits PNK and just votes “not doge” whenever it is drawn.
As a rough heuristic, imagine that we give such an attacker one vote in each case but, for simplicity, all of the existing votes still count and the outcomes of the cases are assumed not to change (after all, if this attacker had resulted in unjust outcomes, those could have been appealed). Then, if we denote by Ni and Di the number of “not doge” and “doge” votes in the ith case respectively, and if d is the deposit lost by incoherent jurors, the attacker's net returns are given by:
Based on the observed values of Di and Ni for each case (up through the cutoff to qualify for a payout of Dogecoins at disputeID 148), we compute that S=-48.9d, namely that such a strategy would have lost 48.9 more deposits than the PNK that it gained back. (Always voting “doge” is even worse; the equivalent calculation gives S=-78.3d.) This strategy essentially does not work as an attacker does not gain anything when she votes with a unanimous decision, and we have seen that most of the cases were, in fact, unanimous.
A more complete answer to this question would depend on what percentage of the total PNK deposited the attacker controlled; then we could consider the attacker's chance of being drawn in the ith case and calculate her expected return. However, we can perform a slightly more nuanced heu...