Monotonicity criterion in order to remove them from office, since the senators serve for life. Limitations on their use. Legal fictions derive their legitimacy from tradition and precedent, rather than formal standing as a source of law. Historically, many legal fictions were created as ad hoc remedies forged to meet a harsh or an unforeseen situation. Conventions and practices over the centuries have imparted a degree of stability both to the institution of legal fictions and to specific legal fictions (such as adoptions and corporate personhood) that have been repeatedly invoked in judicial precedents. While judiciaries retain discretion in the use of 	Legal fiction
5013774	legal fictions, some general propositions regarding the appropriateness of using legal fictions might be expressed as follows: Legal fiction A legal fiction is a fact assumed or created by courts, which is then used in order to help reach a decision or to apply a legal rule. The concept is used almost exclusively in common law jurisdictions, particularly in England. Development of the concept. A legal fiction typically allows the court to ignore a fact that would prevent it from exercising its jurisdiction by simply assuming that the fact is different. In cases where the court must determine whether a 	Legal fiction
5013775	XLR XLR XLR may refer to: XLR XLR may refer to: 	XLR
5013776	Candas Jane Dorsey Candas Jane Dorsey Candas Jane Dorsey (born November 16, 1952) is a Canadian poet and science fiction novelist who resides in her hometown of Edmonton, Alberta. Dorsey became a writer from an early age and works across genre boundaries, writing poetry, fiction, mainstream and speculative, short and long form, arts journalism and arts advocacy. Dorsey has also written television and stage scripts, magazine and newspaper articles, and reviews. Dorsey currently teaches and holds workshops and readings. She has served on the executive board of the Writers' Guild of Alberta and is a founder of SF Canada. In 1998, Dorsey received 	Candas Jane Dorsey
5013777	the Prix Aurora Award. Dorsey was editor-in-chief of The Books Collective (River, Slipstream and Tesseract Books) from 1992 through 2005. Candas Jane Dorsey Candas Jane Dorsey (born November 16, 1952) is a Canadian poet and science fiction novelist who resides in her hometown of Edmonton, Alberta. Dorsey became a writer from an early age and works across genre boundaries, writing poetry, fiction, mainstream and speculative, short and long form, arts journalism and arts advocacy. Dorsey has also written television and stage scripts, magazine and newspaper articles, and reviews. Dorsey currently teaches and holds workshops and readings. She has 	Candas Jane Dorsey
5013778	Monotonicity criterion Monotonicity criterion The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot). That is to say, in single winner elections no winner is harmed by up-ranking and no loser is helped by down-ranking. Douglas R. Woodall called 	Monotonicity criterion
5013779	the criterion mono-raise. Raising a candidate on some ballots while changing" the orders of other candidates does "not" constitute a failure of monotonicity. E.g., harming candidate by changing some ballots from to would violate the monotonicity criterion, while harming candidate by changing some ballots from to would not. The monotonicity criterion renders the intuition that there should be neither need to worry about harming a candidate by (nothing else than) up-ranking nor it should be possible to support a candidate by (nothing else than) counter-intuitively down-ranking. There are several variations of that criterion; e.g., what Douglas  R. Woodall called "mono-add-plump": A candidate should not be harmed if further ballots are added that have top with no second choice. Noncompliance with the monotonicity criterion doesn't tell anything about the likelihood of monotonicity violations, failing in one of a million possible elections would be as well a violation as missing the criterion in any possible election. Of the single-winner ranked voting systems, Borda, Schulze, ranked pairs, maximize affirmed majorities, descending solid coalitions, and descending acquiescing coalitions are monotonic, while Coombs' method, runoff voting, and instant-runoff voting (IRV) are not. The multi-winner single  transferable vote (STV) system is also non-monotonic. While Woodall articulated monotonicity in the context of ordinal voting systems, the property can be generalized to cardinal voting and plurality voting systems by evaluating whether reducing or removing support for a candidate can help that candidate win an election. In this context, first past the post, approval voting, range voting, STAR Voting, majority judgment, as well as the multiple-winner systems single non-transferable vote, plurality-at-large voting (multiple non-transferable vote, bloc voting), Proportional approval voting, Sequential proportional approval voting, Reweighted range voting and cumulative voting are monotonic. Party -list proportional representation using D'Hondt, Sainte-Laguë or the largest remainder method is monotonic in the same sense. Instant-runoff voting and the two-round system are not monotonic. Using an example that applies to instant-runoff voting (IRV) and to the two-round system, it is shown that these voting systems violate the mono-raise criterion. Suppose a president were being elected among three candidates, a left, a right, and a center candidate, and 100 votes cast. The number of votes for an absolute majority is therefore 51. Suppose the votes are cast as follows: According to the 1st  preferences, Left finishes first with 35 votes, Right gets 33 votes, and Center 32 votes, thus all candidates lack an absolute majority of first preferences. In an actual runoff between the top two candidates, Left would win against Right with 30+5+16=51 votes. The same happens (in this example) under IRV, Center gets eliminated, and Left wins against Right with 51 to 49 votes. But if at least two of the five voters who ranked Right first, and Left second, would raise Left, and vote 1st Left, 2nd Right; then Right would be defeated by these votes  in favor of Center. Let's assume that two voters change their preferences in that way, which changes two rows of the table: Now Left gets 37 first preferences, Right receives 31 first preferences, and Center still receives 32 first preferences, and there is again no candidate with an absolute majority of first preferences. But now Right is eliminated, and Center remains in round 2 of IRV (or the actual runoff in the Two-round system). And Center beats its opponent Left with a remarkable majority of 60 to 40 votes. Estimated likelihood of IRV lacking monotonicity. Crispin Allard argued , based on a mathematical model of London voters that the probability of monotonicity failure actually changing the result of an STV multi-winner election for any given constituency would be 1 in 4000, however Warren D. Smith claims that this paper contains 2 computation errors and omits a type of nonmonotonicity, making Allard's result "1000 times smaller than the truth". Lepelley "et al." found a probability of for 3-candidate single-winner elections (vs 11.65% for Coombs' method). Another result, using the (unrealistic) "impartial culture" probability model, yields about 15% probability in elections with 3 candidates. As the number  of candidates increases, these probabilities tend to increase eventually toward 100% (in some models this limit has been proven, in others it is only conjectured). Other Monte Carlo experiments found probabilities of 5.7% for an IAC model, and 6.9% for a uniformly-distributed 1D political spectrum model. Nicholas Miller also disputed Allard's conclusion and provided a different mathematical model for the three-candidate case. A 2013 study using a 2D spatial model with various voter distributions found that IRV was non-monotonic in at least 15% of competitive elections, increasing with number of candidates. The authors conclude that "three -way competitive races will exhibit unacceptably frequent monotonicity failures" and "In light of these results, those seeking to implement a fairer multi-candidate election system should be wary of adopting IRV." Real-life monotonicity violations. If the ballots of a real election are released, it is fairly easy to prove if would have been possible (nothing else is altered on any ballot). Both events can be considered as real-life monotonicity violations. However, the ballots (or information allowing them to be reconstructed) are rarely released for ranked voting elections, which means there are few recorded monotonicity violations for real elections . 2009 Burlington, Vermont mayoral election. A monotonicity violation could have occurred in the 2009 Burlington, Vermont mayor election under instant-runoff voting (IRV), where the necessary information is available. In this election, the winner Bob Kiss could have been defeated by raising him on some of the ballots. For example, if all voters who ranked Republican Kurt Wright over Progressive Bob Kiss over Democrat Andy Montroll, would have ranked Kiss over Wright over Montroll, and additionally some people who ranked Wright but not Kiss or Montroll, would have ranked Kiss over Wright, then these votes in favor of Kiss would  have defeated him. The winner in this scenario would have been Andy Montroll, who was also the Condorcet winner according to the original ballots, i.e. for any other running candidate, a majority ranked Montroll above the competitor. This hypothetical monotonicity violating scenario, however, would require that right-leaning voters switch to the most left-wing candidate. Australian elections and by-elections. Since every or almost every IRV election in Australia has been conducted in the black (i.e. not releasing enough information to reconstruct the ballots), non-monotonicity is difficult to detect in Australia. However, the theoretical disadvantage of non-monotonicity  can be seen in the 2009 Frome state by-election. The by-election was a contest between the Liberal Party of Australia, Australian Labor Party, independent candidate Geoff Brock, and the National Party of Australia. The eventual winner was Brock, who placed only third on first preferences with about 24% of the vote. However, he was favoured by National Party voters, whose preferences placed him ahead of the Labor candidate by 31 votes. Labor was pushed to third place and eliminated in the next count, with most of their preferences flowing to Brock, allowing him to defeat the Liberal candidate . However, if a number of voters who preferred Liberal had given their first preference to Labor, Brock would have been eliminated in the penultimate count. The final count would have been between the Liberal and Labor candidates, allowing the former to win. For this to happen, between 31 and 321 Liberal voters would have needed to instead vote Labor. This is classic monotonicity violation: a number of Liberal voters unintentionally hurt their most preferred candidate. Monotonicity criterion The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system