Additive and multiplicative properties of scoring methods for preference aggregation

The paper reviews some additive and multiplicative properties of ranking procedures used for generalized tournaments with missing values and multiple comparisons. The methods analysed are the score, generalised row sum and least squares as well as fair bets and its variants. It is argued that generalised row sum should be applied not with a fixed parameter, but a variable one proportional to the number of known comparisons. It is shown that a natural additive property has strong links to independence of irrelevant matches, an axiom judged unfavourable when players have different opponents.

The paradox of the binomial Ixodes ricinus activity and the observed unimodal Lyme borreliosis season in Hungary

The change of ambient temperature plays a key role in determining the run of the annual Lyme season. Our aim was to explain the apparent contradiction between the annual unimodal Lyme borreliosis incidence and the bimodal Ixodes ricinus tick activity run – both observed in Hungary – by distinguishing the temperaturedependent seasonal human and tick activity, the temperature-independent factors, and the multiplicative effect of human outdoor activity in summer holiday, using data from Hungary in the period of 1998–2012. This separation was verified by modeling the Lyme incidence based on the separated factors, and comparing the run of the observed and modeled incidence. We demonstrated the bimodality of tick season by using the originally unimodal Lyme incidence data. To model the outdoor human activity, the amount of camping guest nights was used, which showed an irregular run from mid-June to September. The human outdoor activity showed a similar exponential correlation with ambient temperature to that what the relative incidence did. It was proved that summer holiday has great influence on Lyme incidence.

The paradox of the binomial Ixodes ricinus activity and the observed unimodal Lyme borreliosis season in Hungary

The change of ambient temperature plays a key role in determining the run of the annual Lyme season. Our aim was to explain the apparent contradiction between the annual unimodal Lyme borreliosis incidence and the bimodal Ixodes ricinus tick activity run – both observed in Hungary – by distinguishing the temperaturedependent seasonal human and tick activity, the temperature-independent factors, and the multiplicative effect of human outdoor activity in summer holiday, using data from Hungary in the period of 1998–2012. This separation was verified by modeling the Lyme incidence based on the separated factors, and comparing the run of the observed and modeled incidence. We demonstrated the bimodality of tick season by using the originally unimodal Lyme incidence data. To model the outdoor human activity, the amount of camping guest nights was used, which showed an irregular run from mid-June to September. The human outdoor activity showed a similar exponential correlation with ambient temperature to that what the relative incidence did. It was proved that summer holiday has great influence on Lyme incidence.