This paper experimentally investigates whether subjects learn, from their limited experiences, something about the underlying relationship between their nominal voting weights and expected payoffs in weighted voting games. In each session of the experiment, subjects are repeatedly asked to choose one of two 4-player weighted voting games where three out of four players are fictive. After each choice, payoffs for players are determined automatically according to a theory of voting power. We, however, vary the amount of feedback about the payoffs that subjects receive after each choice. The choice problem of games is changed to another one in the second part of the session. The main findings are as follows. (1) The fraction of subjects who chose the weighted voting games that generate higher expected payoffs increased even in the treatment without any immediate feedback on realized payoffs. (2) A statistically significant evidence of “meaningful learning” between two choice problems was observed only in the treatment without immediate feedback.