Some basic models in science are not grounded in what we know but in careful specifying of the limits of our ignorance. Boundary conditions on the conceptually possible range determine whether a distribution is likely to be closer to normal or lognormal and whether arithmetic or geometric means should be used. If finite and non-zero boundary values can be defined, then most actual cases tend to be around the center of the possible range. This approach makes it possible to estimate the number of parties in a national assembly within a factor of two, using only assembly size and electoral district magnitude. Deviations from ignorance-based base line are a signal to look for specifically political causes. This approach may be of use in many aspects of political science.

Effective magnitude (M') and effective threshold (T') are important because they try to express quantitatively a major aspect of electoral systems, namely the degree of squeeze they put on representation of small parties. Three relationships have previously been proposed between M' and T'. Of these, T'=75%(M'+1) is found here to have the most desirable characteristics. However, regardless of the precise equation used, a disturbing discrepancy is observed in the case of single-member districts: the effective threshold predicted is much too high, if applied nationwide. This points out a more general need to keep district-level and nationwide indicators carefully separate. An appendix proposes a new formula to find effective magnitude when district magnitudes within a country vary.

AbstractGaines and Taagepera [(2013) How to operationalize two-partyness. Journal of Elections Public Opinion and Parties, 23(4), pp. 387-404] propose two indices of two-party competition for district-level data, both of which are alleged to be flawed. The case against them rests mainly on whether or not elections with one dominant party should be regarded as exhibiting one- or two-way competition. For those inclined to see 90-10% and 50-50% outcomes are different in kind, our indices can provide better measures than the popular effective number of parties or the "gap". We agree that assessment of a set of outcomes, in a given election or over time, requires careful attention to the important distinction between micro-level data and aggregate measures. © 2014 Elections, Public Opinion & Parties.