Another probability model, the "impartial culture", yields about 15% probability. In elections with more than 3 candidates, these probabilities tend to increase eventually toward 100% (in some models this limit has been proven, in others it is only conjectured). Estimates of 5–15% order are easily confirmed in any probability model with Monte Carlo experiments and the aid of the "was it monotonic?" tests stated in the Lepelley paper. Nicholas Miller also disputed Allard's conclusion and provided a different mathematical model. A 2013 study using a spatial model 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." 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. 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. 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 in 2009, the theoretical disadvantage of non-monotonicity worked out in practice in the 2009 Frome state by-election, in an election between the National Party of Australia, the Australian Labor Party, the Australian Liberal Party and Independent candidate Geoff Brock.