Single-peaked preferences are the workhorse domain restriction in social choice: each agent has a preferred level of a public good, and utility decreases monotonically in distance from this peak. The restriction enables strategy-proof mechanisms — honest voting is optimal — which is impossible on unrestricted domains.
But real committees include members who genuinely don't care. Not strategic abstainers gaming the system — truly indifferent agents for whom any outcome is equally acceptable. The standard single-peaked framework can't represent them: a single-peaked preference must have a peak somewhere.
This paper augments the domain with complete indifference and characterizes the resulting strategy-proof mechanisms. They are target rules with a default: each agent either reports a peak or declares indifference, and the rule selects a target level adjusted by the indifferent agents' abstention. Onto-ness and pairwise strategy-proofness are necessary and sufficient.
The characterization shows that adding “I don't care” as a legitimate response doesn't destroy the tractability of single-peaked domains — it refines it. The default handles the indifferent agents; the target rule handles the opinionated ones. The mechanism accommodates genuine apathy without being exploitable by strategic apathy.