Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

In the line opened by Kalai and Muller (1997), we explore new conditions on prefernce domains which make it possible to avoid Arrow's impossibility result. In our main theorem, we provide a complete characterization of the domains admitting nondictorial Arrovian social welfare functions with ties (i.e. including indifference in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach first applied to social choice theory by Sethuraman, Teo and Vohra ((2003), (2006)). In order to obtain a representation of Arrovian social welfare functions whose range can include indifference, we generalize Sethuraman et al.'s work and specify integer programs in which variables are allowed to assume values in the set {0, 1/2, 1}: indeed, we show that, there exists a one-to-one correspondence between solutions of an integer program defined on this set and the set of all Arrovian social welfare functions - without restrictions on the range.

Integer Programming on Domains Containing Inseparable Ordered Paris

Using the integer programming approach introduced by Sethuraman, Teo, and Vohra (2003), we extend the analysis of the preference domains containing an inseparable ordered pair, initiated by Kalai and Ritz (1978). We show that these domains admit not only Arrovian social welfare functions \without ties," but also Arrovian social welfare functions \with ties," since they satisfy the strictly decomposability condition introduced by Busetto, Codognato, and Tonin (2012). Moreover, we go further in the comparison between Kalai and Ritz (1978)'s inseparability and Arrow (1963)'s single-peak restrictions, showing that the former condition is more \respectable," in the sense of Muller and Satterthwaite (1985).

Picking the Right Budget Constraint for Scotland

This position paper considers the devolution of further fiscal powers to the Scottish Parliament in the context of the objectives and remit of the Smith Commission. The argument builds on our discussion of fiscal decentralization made in our previous published work on this topic. We ask what sort of budget constraint the Scottish Parliament should operate with. A soft budget constraint (SBC) allows the Scottish Parliament to spend without having to consider all of the tax and, therefore, political consequences, of that spending, which is effectively the position at the moment. The incentives to promote economic growth through fiscal policy – on both the tax and spending sides are weak to non-existent. This is what the Scotland Act, 1998, and the continuing use of the Barnett block grant, gave Scotland. Now other budget constraints are being discussed – those of the Calman Commission (2009) and the Scotland Act (2012), as well as the ones offered in 2014 by the various political parties – Scottish Conservatives, Scottish Greens, Scottish Labour, the Scottish Liberal Democrats and the Scottish Government. There is also the budget constraint designed by the Holtham Commission (2010) for Wales that could just as well be used in Scotland. We examine to what extent these offer the hard budget constraint (HBC) that would bring tax policy firmly into the realm of Scottish politics, asking the Scottish electorate and Parliament to consider the costs to them of increasing spending in terms of higher taxes; or the benefits to them of using public spending to grow the tax base and own-sourced taxes? The hardest budget constraint of all is offered by independence but, as is now known, a clear majority of those who voted in the referendum did not vote for this form of budget constraint. Rather they voted for a significant further devolution of fiscal powers while remaining within a political and monetary union with the rest of the UK, with the risk pooling and revenue sharing that this implies. It is not surprising therefore that none of the budget constraints on offer, apart from the SNP’s, come close to the HBC of independence. However, the almost 25% fall in the price of oil since the referendum, a resource stream so central to the SNP’s economic policy making, underscores why there is a need for a trade off between a HBC and risk pooling and revenue sharing. Ranked according to the desirable characteristic of offering something approaching a HBC the least desirable are those of the Calman Commission, the Scotland Act, 2012, and Scottish Labour. In all of these the ‘elasticity’ of the block grant in the face of failure to grow the Scottish tax base is either not defined or is very elastic – meaning that the risk of failure is shuffled off to taxpayers outside of Scotland. The degree of HBC in the Scottish Conservative, Scottish Greens and Scottish Liberal Democrats proposals are much more desirable from an economic growth point of view, the latter even embracing the HBC proposed by the Holtham Commission that combines serious tax policy with welfare support in the long-run. We judge that the budget constraint in the SNP’s proposals is too hard as it does not allow for continuation of the ‘welfare union’ in the UK. We also consider that in the case of a generalized UK economic slow requiring a fiscal stimulus that the Scottish Parliament be allowed increased borrowing to be repaid in the next economic upturn.