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However, the subtle differences between different<jats:inline-formula><jats:alternatives><jats:tex-math>$$ ML $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>ML<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>schemes are often overlooked. Two canonical subsets of<jats:inline-formula><jats:alternatives><jats:tex-math>$$ ML $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>ML<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>schemes are \"Image missing\"schemes (which only depend on unweighted majority comparisons) and \"Image missing\"schemes (which only depend on weighted majority comparisons). We prove that \"Image missing\"schemes are the only homogeneous<jats:inline-formula><jats:alternatives><jats:tex-math>$$ ML $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>ML<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>schemes that satisfy<jats:inline-formula><jats:alternatives><jats:tex-math>$$ SD $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>SD<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-efficiency and<jats:inline-formula><jats:alternatives><jats:tex-math>$$ SD $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>SD<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-participation, but are also among the most manipulable<jats:inline-formula><jats:alternatives><jats:tex-math>$$ ML $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>ML<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>schemes. While all<jats:inline-formula><jats:alternatives><jats:tex-math>$$ ML $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>ML<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>schemes are manipulable and even violate monotonicity, they are never manipulable when a Condorcet winner exists and satisfy a relative notion of monotonicity. We also evaluate the frequency of manipulable preference profiles and the degree of randomization of<jats:inline-formula><jats:alternatives><jats:tex-math>$$ ML $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>ML<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>schemes via extensive computer simulations. In summary,<jats:inline-formula><jats:alternatives><jats:tex-math>$$ ML $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>ML<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>schemes are rarely manipulable and often do not randomize at all, especially for few alternatives. The average degree of randomization of \"Image missing\"schemes is consistently lower than that of \"Image missing\"schemes.<\/jats:p>","DOI":"10.1007\/s00355-021-01326-x","type":"journal-article","created":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T08:02:51Z","timestamp":1624262571000},"page":"5-38","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An analytical and experimental comparison of maximal lottery schemes"],"prefix":"10.1007","volume":"58","author":[{"given":"Florian","family":"Brandl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4179-9897","authenticated-orcid":false,"given":"Felix","family":"Brandt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Stricker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,16]]},"reference":[{"key":"1326_CR1","unstructured":"Aziz H, Brandt F, Brill M (2013) On the tradeoff between economic efficiency and strategy proofness in randomized social choice. 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