  One of the most widespread human behavioral biases is the present bias -- the
tendency to overestimate current costs by a bias factor. Kleinberg and Oren
(2014) introduced an elegant graph-theoretical model of inconsistent planning
capturing the behavior of a present-biased agent accomplishing a set of
actions. The essential measure of the system introduced by Kleinberg and Oren
is the cost of irrationality -- the ratio of the total cost of the actions
performed by the present-biased agent to the optimal cost. This measure is
vital for a task designer to estimate the aftermaths of human behavior related
to time-inconsistent planning, including procrastination and abandonment.
  As we prove in this paper, the cost of irrationality is highly susceptible to
the agent's choices when faced with a few possible actions of equal estimated
costs. To address this issue, we propose a modification of Kleinberg-Oren's
model of inconsistent planning. In our model, when an agent selects from
several options of minimum prescribed cost, he uses a randomized procedure. We
explore the algorithmic complexity of computing and estimating the cost of
irrationality in the new model.
