We build a political economy model where individuals differ in the extent of the behavioral bias they exhibit when voting first over social long-term care (LTC) insurance and then choosing the amount of LTC annuities. LTC annuities provide a larger return if dependent than if healthy. We study the majority voting equilibrium under three types of behavioral biases: myopia, optimism and sophisticated procrastination. Optimists and myopics similarly under-estimate their own dependency risk both when voting and when buying LTC annuities. They differ in that optimists know the correct average dependency risk (that determines the return of both social and private insurance), while myopics also under-estimate this average risk (and thus over-estimate the insurance return). Sophisticated procrastinators act as if they under-estimated their own risk when buying annuities, but anticipate this bias at the time of voting. We obtain that the stylized observation of lack of LTC insurance is compatible with agents being optimistic or myopic, but not sophisticated procrastinators. Increasing the difference in return across dependency states for the LTC annuity is detrimental to sophisticated voters and to very biased myopic and optimist voters. Finally, less myopic individuals may end up worse off, at the majority-voting equilibrium, than more myopic agents, casting some doubt on the usefulness of information campaigns.