Final answer:
Statements i and iv are the two incorrect statements regarding decision-making under uncertainty and risk. Statement i incorrectly characterizes uncertainty with probabilistic elements, and Statement iv mistakenly regards a dearth of risk information as certainty and known risk distribution as deterministic.
Step-by-step explanation:
The question asks which two of the provided statements regarding decision-making under conditions of certainty, risk, and uncertainty are incorrect. Upon A two of the statements are indeed incorrect: Statement i, which suggests that decisions under uncertainty are primarily characterized by probabilistic states of nature and payoff functions, is incorrect because decisions under uncertainty are characterized by not knowing either the probabilities or the outcomes. This also leads to the incorrectness of the second part of the statement, which claims that decisions under risk have broad uncertainties, when in fact they involve known probabilities but unknown outcomes. Statement iv is also incorrect, as it suggests that a lack of information on risk distribution indicates certainty in decision-making, which is a misunderstanding of the term 'certain', and that known measures of risk distribution make decision-making deterministic, which is not necessarily true as risk entails a lack of certainty about outcomes despite having probabilities associated with them.