We consider the problem of manipulation under an assumption of incomplete information with bounded rationality of voters. The main two competing models of higher-level reasoning are compared: level-k model (where manipulators believe that others are exactly level-(k-1)), and cognitive hierarchy model (where others are at most level-(k-1)). We define manipulation in a safe sense, as the existence of a strategy that guarantees no worse outcome while allowing improvement in some scenarios. We study how zero manipulability is obtained in both models, as well as the cyclicity and stabilization of manipulation probabilities. Finally, we illustrate our results by computing exact manipulation probabilities across key parameters: information types, reasoning models, voting rules, and profile size.

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