This document discusses different vote-processing rules that can be used to combine rankings from multiple epidemiological models when evaluating control interventions for foot-and-mouth disease outbreaks. It analyzes four voting rules - first-past-the-post, Borda count, Coombs method, and alternative vote - using rankings from four models on five interventions based on minimizing cattle culled and outbreak duration. All voting rules identified the same best intervention, showing these rules may be useful approaches when multiple models inform decision-making by avoiding direct comparison of non-comparable model metrics.

1. 1EuFMD | Open Session special edition | #OS20se
William Probert1, Sam Nicol2, Matthew J Ferrari3, Shou-li Li4,
Katriona Shea3, Michael J Tildesley5, Michael C Runge6
1 University of Oxford, Oxford, UK;
2 CSIRO Land and Water, QLD, Australia;
3 The Pennsylvania State University, PA, USA;
4 Lanzhou University, Lanzhou, People's Republic of China.;
5 University of Warwick, Coventry, CV4 7AL, UK;
6 US Geological Survey, MA, USA
Vote-processing rules for combining
rankings of control interventions from
multiple models

2. 2EuFMD | Open Session special edition | #OS20se
• Simulation models are often used for informing decision-making in response to FMD outbreaks.
• When using multiple models, what is the best method of combining recommendations across models?
Approaches for combining model recommendations to compare control interventions:
• Assumes model outputs can be
directly compared across models
• Makes no assumption about
comparability of model outputs
• Only compares rankings of
interventions across models
AIMS:
• We evaluate four voting rules for
combining rankings across models

3. 3EuFMD | Open Session special edition | #OS20se
Objective
Intervention 1st 2nd 3rd 4th 5th
Minimize total cattle culled
(head)
IP 16.3 19.5 31.0 14.8 18.3
IPDC 7.5 8.3 16.8 45.9 21.6
RC3 3.8 2.8 12.0 25.1 56.4
V3 30.3 36.3 21.6 9.3 2.5
V10 42.1 33.1 18.5 5.0 1.3
Minimize outbreak duration
(days)
IP 7.0 17.5 22.3 22.3 30.8
IPDC 11.5 19.8 19.5 24.6 24.6
RC3 55.9 8.5 7.0 12.3 16.3
V3 11.3 24.1 27.1 23.1 14.5
V10 14.2 30.1 24.1 17.8 13.8
IP culling
IPDC culling
Ring culling
(3km)
Ring vaccination
(3km)
Ring vaccination
(10km)
IP = infected premises
DC = dangerous contacts
Results
• Four models (NAADSM, Warwick, AusSpread, Interspread Plus)
• Hypothetical outbreak in county in UK
• Same initial conditions
• 5 interventions
• Interventions ranked on two measures:
total cattle culled & outbreak duration
Four voting rules process these rankings:
• First-past-the-post
• Borda Count
• Coombs Method
• Alternative Vote
All voting rules chose the same best intervention
as when ranking on mean projections.
Simulations

4. 4EuFMD | Open Session special edition | #OS20se
• Vote-processing rules avoid comparing models on metrics
that are not consistently generated across models.
Vote-processing rules are:
• Simple to implement and understand
• Straight-forward to compute
• Trusted to determine winners in government elections
• Vote-processing rules may be useful when multiple models
are used to inform decision-making
IP culling
IPDC culling
Ring culling
(3km)
Ring vaccination
(3km)
Ring vaccination
(10km)
Tie
Alternative VoteCoombs MethodBorda CountFPP
Percentofexperimentswith
interventionchosenaswinner
0
100
0
100
Number of models added with interventions randomly ranked
1 50 1 50 1 50 1 50
Outbreak
duration
Cattle
culled
Results: sensitivity analysis Summary