People's satisfaction from some goods and services depends on their relative as distinct from their absolute position as consumers. Such items are called "positional goods", and a restriction of their supply in the situation of general income growth is conducive to expenditure escalation as in an arms race. If education is a positional good in this sense, arrangements are needed that will best prevent such an outcome. The introduction of education vouchers of a value egual to the average per capita public school expenditure, it is argued, will only hinder not help. This is because some recipients will be tempted to obtain more education with marginal additions to their vouchers from their own pockets. Vouchers are thus welfare reducing because they encourage rather than discourage "arms race" situations. Using a formal median voter model we show that concerns over possible escalation of expenditure will prompt a majority of voters to reject a universal voucher system. We examine, as an alternative, a selective voucher system that will remove the escalation problem. Under this system only low-income families will receive vouchers. We demonstrate that the median voter will favor such a selective voucher system provided that the voucher-induced increase in competition lowers costs and/or improves guality of education.