Does Evidential Decision Theory really fail Solomon's Problem?



Solomon's Problem and varients thereof are often cited as criticism of Evidential decision theory.

For background, here's Solomon's Problem: King Solomon wants to sleep with another man's wife. However, he knows that uncharismatic leaders frequently sleep with other men's wives, and charismatic leaders almost never do. Furthermore, uncharismatic leaders are frequently overthrown, and charismatic leaders rarely are. On the other hand, sleeping with other men's wives does not cause leaders to be overthrown. Instead, high charisma decreases the chance that a leader will sleep with another man's wife and the chance that the leader will be overthrown separately. Not getting overthrown is more important to King Solomon than getting the chance to sleep with the other guy's wife.

Causal decision theory holds that King Solomon can go ahead and sleep with the other man's wife because it will not directly cause him to be overthrown. Timeless decision theory holds that he can sleep with the woman because it will not cause his overthrow in any timeless sense either. Conventional wisdom holds that Evidential decision theory would have him refrain from her, because updating on the fact that he slept with her would suggest a higher probability that he will get overthrown.

The problem with that interpretation is that it assumes that King Solomon only updates his probability distributions based on information about him that is accessible to others. He cannot change whether or not he would sleep with another man's wife given no other disincentives by refraining from doing so in response to other disincentives. The fact that he is faced with the dilemma already indicates that he would. Updating on this information, he knows that he is probably uncharismatic, and thus likely to get overthrown. Updating further on his decision after taking into account the factors guiding his decision will not change the correct probability distribution.

This more complete view of Evidential decision theory is isomorphic to Timeless decision theory (edit: shown to be false in comments). I'm slightly perplexed as to why I have not seen it elsewhere. Is it flawed? Has it been mentioned elsewhere and I haven't noticed? If so, why isn't it so widely known?