One of the postulates of infra-Bayesianism is the maximin decision rule. Given a crisp infradistribution $\Theta$, it defines the optimal action to be:

$$a^{\ast }\left(\Theta \right):=\arg \underset{a}{max}\underset{\mu \in \Theta }{min}{E}_{\mu }\left[U\right(a\left)\right]$$

Here $U$ is the utility function.

What if we use a different decision rule? Let $t\in [0,1]$ and consider the decision rule

$$a_t^{\ast }\left(\Theta \right):=\arg \underset{a}{max}\left(t\underset{\mu \in \Theta }{min}{E}_{\mu }\right[U\left(a\right)]+(1-t\left)\underset{\mu \in \Theta }{max}{E}_{\mu }\right[U\left(a\right)\left]\right)$$

For $t=1$ we get the usual maximin ("pessimism"), for $t=0$ we get maximax ("optimism") and for other values of $t$ we get something in the middle (we can call "$t$-mism").

It turns out that, in some sense, this new decision rule is actually reducible to ordinary maximin! Indeed, set

$${\mu }_t^{\ast }:=\arg \underset{\mu }{max}{E}_{\mu }\left[U\right(a_t^{\ast }\left)\right]$$

$${\Theta }_t:=t\Theta +(1-t){\mu }_t^{\ast }$$

Then we get

$$a^{\ast }\left({\Theta }_t\right)=a_t^{\ast }\left(\Theta \right)$$

More precisely, any pessimistically optimal action for ${\Theta }_t$ is $t$-mistically optimal for $\Theta$ (the converse need not be true in general, thanks to the arbitrary choice involved in ${\mu }_t^{\ast }$).

To first approximation it means we don't need to consider $t$-mistic agents since they are just special cases of "pessimistic" agents. To second approximation, we need to look at what the transformation of $\Theta$ to ${\Theta }_t$ does to the prior. If we start with a simplicity prior then the result is still a simplicity prior. If $U$ has low description complexity and $t$ is not too small then essentially we get full equivalence between "pessimism" and $t$-mism. If $t$ is small then we get a strictly "narrower" prior (for $t=0$ we are back at ordinary Bayesianism). However, if $U$ has high description complexity then we get a rather biased simplicity prior. Maybe the latter sort of prior is worth considering.