Two conditions for the application of Lorenz curve and Gini coefficient to voting and allocated seats

The Lorenz curve and Gini coefficient are applied here to measure and graph disproportionality in outcomes for multiseat elections held in 2017. The discussion compares Proportional Representation (PR) in Holland (PR Gini 3.6%) with District Representation (DR) in France (41.6%), UK (15.6%) and Northern Ireland (NI) (36.7%). In France the first preferences of voters for political parties show from the first round in the two rounds run-off election. In UK and NI the first preferences of voters are masked because of strategic voting in the single round First Past the Post system. Thus the PR Gini values for UK and NI must be treated with caution. Some statements in the voting literature hold that the Lorenz and Gini statistics are complex to construct and calculate for voting. Instead, it appears that the application is actually straightforward. These statistics appear to enlighten the difference between PR and DR, and they highlight the disproportionality in the latter. Two conditions are advised to enhance the usefulness of the statistics and the comparability of results: (1) Order the political parties on the ratio (rather than the difference) of the share of seats to the share of votes, (2) Use turnout as the denominator for the shares, and thus include the invalid and wasted vote (no seats received) as a party of their own. The discussion also touches upon the consequences of disproportionality by DR. Quite likely Brexit derives from the UK system of DR and the discontent about (mis-) representation. Likely voting theorists from countries with DR have a bias towards DR and they are less familiar with the better democratic qualities of PR.