Formally, Ulysses faced a problem of time inconsistency in his optimal plan. His optimal plan was to listen to the Sirens and then continue his journey. But this was time inconsistent, because once he had embarked on the plan by listening to the Sirens he would not be able to implement the later part of the plan, the rest of his journey. By contrast, a time consistent optimal plan is one that specifies a sequence of actions (At, At+1, At+2 and so on), one for each moment in time (T, T+1, T+2 and so on), which enjoys the property that the individual will actually choose in each time period the action specified by the plan. Thus, when T+1 occurs, having undertaken At in T, the individual will still choose At+1 as the best action rather than some other, and so on.
The time-inconsistency arises because the Sirens affect Ulysses’ preferences. His perception of the best action changes in the middle of the plan and this leads him to deviate from the original version. Ulysses implemented his optimal plan by denying himself freedom at the later stage of the plan. Having instructed his men to tie him to the mast and to ignore any orders to do anything other than sail past the rocks, he told them to plug their ears and row.
Thus, Ulysses established for himself a private constitution, a set of more or less binding rules that constrained his future choices. By exploiting elements of his natural and social environment, Ulysses was able to subvert certain inclinations of his future self, inclinations that he knew would be destructive to his overall interests but which would nevertheless prove irresistible when they arose.
[Likewise], the principal issue for constitutional political economy is that of forming a mutually agreeable constitution for social arrangements among a community of persons. Ulysses is therefore to be seen not merely as a single actor but more particularly as representing society as a whole, and the mast and rope are to be identified as the rules by which ordered society is governed.
– Ludwig Van den Hauwe on Constitutional Political Economy