We consider a two-period irreversible investment decision problem in which the firm can either invest in period 0 or in period 1. The firm is assumed to be able to specify a set of three scenarios or more but not a probability measure. Assuming the option to wait is valued with the no-arbitrage principle, when the firm makes use of the criteria α-maxmin, we show the firm ends up with a known probability measure that assigns a positive probability to three or four scenarios only.