and 3/6 to Mexico for graft, while on a much less representative survey such as BERI which covers primarily developed countries, Mexico receives a rather poor rating of 1/7.

What can be done about these non-linearities? A very general solution to this problem might be to combine only the ordinal information in each indicator, i.e. the relative rankings of countries within each indicator. In particular, one can think of a given indicator as providing a ranking of pairs of countries according to their level of governance. The information in the relative rankings of countries from various indicators can then be combined by noting that if several indicators consistently rank country A as having better govemance than country B, this provides evidence that governance is in fact better in country A than in country B. Clearly, this approach has several advantages. First, it is computationally very simple. Second, we do not have to know the choice of units in which governance is measured , or whether indicators are representative or not. Third, it does not require any assumption of linearity in the relationship between governance and observed scores. However, this method will result.in larger standard errors for pairwise comparisons since it discards information in differences in the level of scores across countries and indicators.15 To illustrate the relative imprecision of such an ordinal aggregate, for every pair of countries j and j' on every indicator k, we construct an indicator variable x0j,j',k) which takes the value 1 if country j is ranked higher than country j' with respect to the aspect of governance covered by indicator k, and zero otherwise.16 A natural null hypothesis to test is that governance in countries jand j' is the same, i.e. that the probability x(,j',k) is equal to one is 0.5. Under the assumption that the errors are independent across 15 A further drawback of this method is that it is difficult to construct an aggregate ranking of countries according to governance. One possibility would be to average the indicator variables x0,j',k) over all surveys k and partner countries j', and rank oDuntries according to this index. However, it is difficult to put standard errors on such a ranking, since even if the errors are independent across surveys, the x(,j',k) will not be independent across partner countries j'. A deeper problem with this method is that there is a fundamental result from social choice theory which places strong restrictions on the properties such an aggregate ranking may have. According to Arrow's Impossibility Theorem, it is impossible for any aggregation of each indicators' 'preferences" to simultaneiously satisfy three intuitive and desirable properties: (i) the aggregation respects unanimity -- if every indicator says that A is more corrup **t** han B, then so should our aggregate, and (ii) the aggregation displays the independence of irrelevant alternatives property -- the ranking of A and B does not depend on any indicators' ranking bf A or B relative to any other country C; and (iii) the aggregation is non-dictatorial -the aggregate ranking of A and B is not uniquely determined by a single indicators ranking of A and B. In particular, Arrow's theorem tells us that if (i) and (ii) hold, then (iii) does not hold.

16 For those surveys which report discrete categorical scores, we discard 'ties" as uninformative about the relative level of govemance.

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