A consumer is observed making the following choices between three bundles of goods: Bundle A, Bundle B, and Bundle C.

1. When presented with a choice between Bundle A and Bundle B, the consumer chooses Bundle A.
2. When presented with a choice between Bundle B and Bundle C, the consumer chooses Bundle B.
3. When presented with a choice between Bundle A and Bundle C, the consumer chooses Bundle C.

Analyze this consumer's set of choices. Based on the standard assumptions about how individuals consistently rank their options, is this consumer's behavior predictable and logical? Explain which specific assumption of rational preference is being violated, if any, and describe why this pattern of choices creates a problem for representing their preferences with a single, well-defined mathematical function.