Let's assume that it is rational for people to prefer a dam to be built to prevent flooding on farmland, and in fact 100% of 100 farmers privately agree that it is worth it to each of them to pay their share of the cost of the dam.

If there is no vote, but unanimous agreement is required before a project proceeds, then individuals who may secretly want the dam and think it is worth their share of the cost, nonetheless have a selfish incentive to claim that they don't want the dam, so that others pay for it instead of them. So there are societal costs associated with people not telling the truth about their preferences. Namely, projects that may benefit everyone, may be underfunded.

These costs can be reduced in certain voting situations. If the majority preference is enforced and each farmer thinks it is rational to split the cost of building the dam amongst everyone (all 100 farmers), all will in fact vote for it. So voting is valuable in this instance, because it causes the voters to be honest about their preferences.

Do you see why a group of 100 people, all of whom correctly suspect (but don't know) that 100% of everyone else wants to fund a project (like a dam to prevent flooding of their farms), could rationally prefer to vote for a project (with majority rule) rather than meet in a room and negotiate?