= Solution
Write $A$ and $B$ for the two deterministic outcomes. Under the <expected utility hypothesis>, indifference between them implies $u(A)=u(B)=c$. The <expected utility> of the fair <lottery> is consequently
$$
U\left(\tfrac12 A+\tfrac12 B\right)=\tfrac12u(A)+\tfrac12u(B)=c.
$$
It must therefore be indifferent to each deterministic outcome, contradicting the asserted strict preference. \b[These <preferences> do not admit an <expected utility> representation over the stated outcomes.] Equivalently, <affine utility on probability measures> preserves this indifference under mixing, as required by the <independence axiom for lottery preferences>.
A concern for the fairness of the procedure can be perfectly intelligible. It would require enlarging the outcome description to include the procedure; it cannot be represented by an <expected utility> over only the two final gift recipients while retaining the stated strict preference.
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