Page 623 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 623
COMBINATORICS AND DISCRETE MATHEMATICS
A novel non-statistical methodology for detecting gerrymandering in
parallel voting systems
Radu Buzatu, radubuzatu@gmail.com
Moldova State University, Republic of Moldova
Coauthor: Igor Mandric
Gerrymandering is a practice intended to establish a political advantage for a particular party or
group by manipulating electoral district boundaries. Switching from one electoral system to an-
other one is frequently criticized by the opposition and is viewed as a means for the ruling party
to stay in power. In particular, when the new electoral system is a parallel voting (or a single-
member district) system, the ruling party is usually suspected of applying gerrymandering to
increase the chance to win in a maximum possible number of districts.
Since it is extremely challenging to detect gerrymandering by using statistical methods, we
propose a novel non-statistical methodology that has proven effective for detecting gerryman-
dering and computing fair districting under parallel voting systems. Our methodology is based
on identifying the set of all feasible electoral outcomes and comparing the corresponding effi-
ciency scores’ values. For identifying all feasible electoral outcomes, we formulate and solve
several gerrymandering problems as integer linear programming problems.
We showcased the application of our approach to the Moldovan parliamentary elections
of 2019. Our results suggest that contrary to previous studies’ arguments, there is no clear
evidence to consider that the districting map used in those elections was unfair. Importantly,
we also provide an example of the most equitable districting map that does not advantage any
political party over another.
The general position number of classical Sierpin´ ski Graphs
Khadijeh Fathalikhani, fathalikhani.kh@gmail.com
University of Kashan, Kashan, 87317-53153, Islamic Republic of Iran
Coauthor: Azam Babai
Let G be a graph and S be a subset of its vertex set. If no three vertices of S lie on a common
geodesic, then S is called a general position set. Such a set with largest size is a gp-set of G and
its size is the gp-number of G. In this paper, we try to find gp-number of Sierpin´ski Graphs.
Entropy of Ribbon Tilings
Vladislav Kargin, slavakargin@yahoo.com
Binghamton University, United States
I will talk about ribbon tilings, which have been originally introduced and studied by Pak and
Sheffield. These are tilings of a connected region in the square lattice by n-ribbons, – the
sequences of n squares, with the next square appearing only on the right or the upper side of
the previous square. These tilings are a generalization of well-studied domino tilings. I will
explain how ribbon tilings are connected to acyclic orientations on graphs, and present some
results about enumeration of these tilings on some simple regions.
In particular, we have a bound for the growth in the number of ribbon tilings on general
621
A novel non-statistical methodology for detecting gerrymandering in
parallel voting systems
Radu Buzatu, radubuzatu@gmail.com
Moldova State University, Republic of Moldova
Coauthor: Igor Mandric
Gerrymandering is a practice intended to establish a political advantage for a particular party or
group by manipulating electoral district boundaries. Switching from one electoral system to an-
other one is frequently criticized by the opposition and is viewed as a means for the ruling party
to stay in power. In particular, when the new electoral system is a parallel voting (or a single-
member district) system, the ruling party is usually suspected of applying gerrymandering to
increase the chance to win in a maximum possible number of districts.
Since it is extremely challenging to detect gerrymandering by using statistical methods, we
propose a novel non-statistical methodology that has proven effective for detecting gerryman-
dering and computing fair districting under parallel voting systems. Our methodology is based
on identifying the set of all feasible electoral outcomes and comparing the corresponding effi-
ciency scores’ values. For identifying all feasible electoral outcomes, we formulate and solve
several gerrymandering problems as integer linear programming problems.
We showcased the application of our approach to the Moldovan parliamentary elections
of 2019. Our results suggest that contrary to previous studies’ arguments, there is no clear
evidence to consider that the districting map used in those elections was unfair. Importantly,
we also provide an example of the most equitable districting map that does not advantage any
political party over another.
The general position number of classical Sierpin´ ski Graphs
Khadijeh Fathalikhani, fathalikhani.kh@gmail.com
University of Kashan, Kashan, 87317-53153, Islamic Republic of Iran
Coauthor: Azam Babai
Let G be a graph and S be a subset of its vertex set. If no three vertices of S lie on a common
geodesic, then S is called a general position set. Such a set with largest size is a gp-set of G and
its size is the gp-number of G. In this paper, we try to find gp-number of Sierpin´ski Graphs.
Entropy of Ribbon Tilings
Vladislav Kargin, slavakargin@yahoo.com
Binghamton University, United States
I will talk about ribbon tilings, which have been originally introduced and studied by Pak and
Sheffield. These are tilings of a connected region in the square lattice by n-ribbons, – the
sequences of n squares, with the next square appearing only on the right or the upper side of
the previous square. These tilings are a generalization of well-studied domino tilings. I will
explain how ribbon tilings are connected to acyclic orientations on graphs, and present some
results about enumeration of these tilings on some simple regions.
In particular, we have a bound for the growth in the number of ribbon tilings on general
621
