https://doi.org/10.1140/epjb/s10051-024-00742-z
Regular Article - Statistical and Nonlinear Physics
Scheduling meetings: are the odds in your favor?
1
Physics Department, Hamilton College, 13323, Clinton, NY, USA
2
Department of Physics, Case Western Reserve University, 44106-7079, Cleveland, OH, USA
3
Physics Department, University of California, 95064, Santa Cruz, CA, USA
Received:
10
April
2024
Accepted:
28
June
2024
Published online:
13
August
2024
Polling all the participants to find a time when everyone is available is the ubiquitous method of scheduling meetings nowadays. We examine the probability of a poll with m participants and 
possible meeting times succeeding, where each participant rejects r of the options. For large and fixed 
we can carry out a saddle-point expansion and obtain analytical results for the probability of success. Despite the thermodynamic limit of large 
the ‘microcanonical’ version of the problem where each participant rejects exactly r possible meeting times, and the ‘canonical’ version where each participant has a probability 
of rejecting any meeting time, only agree with each other if 
For 
has to be 
for the poll to succeed, i.e., the number of meeting times that have to be polled increases exponentially with m. Equivalently, as a function of p, there is a discontinuous transition in the probability of success at 
. If the participants’ availability is approximated as being unchanging from one week to another, i.e., is limited, a realistic example discussed in the text of the paper shows that the probability of success drops sharply if the number of participants is greater than approximately 4.
© The Author(s) 2024
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