arXiv subjects

Malavika Mukundan

Publications and source records attributed to Malavika Mukundan.

6 recordsLinked to original sources

arXiv2026

Candidate Moderation under Instant Runoff and Condorcet Voting: Evidence from the Cooperative Election Study

This article extends the analysis of Atkinson, Foley, and Ganz in "Beyond the Spoiler Effect: Can Ranked-Choice Voting Solve the Problem of Political Polarization?". Their work uses a one-dimensional spatial model based on survey data from the Cooperative Election Survey (CES) to examine how instant-runoff voting (IRV) and Condorcet methods promote candidate moderation. Their model assumes an idealized electoral environment in which all voters possess complete information regarding candidates' ideological positions, all voters provide complete preference rankings, etc. Under these assumptions, their results indicate that Condorcet methods tend to yield winners who are substantially more moderate than those produced by IRV. We construct new models based on CES data which take into account more realistic voter behavior, such as the presence of partial ballots. Our general finding is that under more realistic models the differences between Condorcet methods and IRV largely disappear, implying that in real-world settings the moderating effect of Condorcet methods may not be nearly as strong as what is suggested by more theoretical models.

econ.GN↗

arXiv2024

A cell decomposition for marked cycle curves

We describe a family $\textrm{Cyc}_p(\mathcal{F})$ of marked cycle curves that parameterize the cycles of period $p$ of a given family $\mathcal{F}$ of dynamical systems. We produce algorithms to compute a canonical cell decomposition for the marked cycle curves over the family $\textrm{Per}_1(0)$ of quadratic polynomials as well as over the family $\textrm{Per}_2(0)$ of quadratic rational maps with a critical 2-cycle. We obtain formulas for the number of $d$-cells in these decompositions, giving rise to e.g. a formula for their genus.

math.DS↗

arXiv2024

Dynamical approximations of postsingularly finite entire maps

We prove that every postsingularly finite entire map $g$ can be approximated by a sequence of postcritically finite complex polynomials $(g_n)$ such that their postsingular dynamics $g|P_g$ and $g_n|P_{g_n}$ are conjugate for every $n \in \mathbb{N}$. To establish this result, we introduce the notion of combinatorial convergence for sequences of entire Thurston maps defined on the topological plane $\mathbb{R}^2$ and having the same marked set $A$. We prove that if such a sequence $(f_n)$ converges combinatorially to a Thurston map $f$, then the sequence of Thurston pullback maps $(σ_{f_n})$ converges to $σ_f$ locally uniformly on the Teichmüller space $\mathrm{Teich}(\mathbb{R}^2, A)$.

math.DS↗

arXiv2023

Dynamical approximation of postsingularly finite exponentials

Given any postsingularly finite exponential function $p_λ(z) = λ\exp(z)$ where $λ\in \C^*$, we construct a sequence of postcritically finite unicritical polynomials $p_{d,λ_d}(z) = λ_d(1+\frac{z}{d})^d$ that converge to $p_λ$ locally uniformly in $\C$, with the same postsingular portrait as that of $p_λ$. We describe $λ_d$ in terms of parameter rays in the space of degree $d$ unicritical polynomials, and exhibit a relationship between the angles of these parameter rays as $d \rightarrow \infty$ and the external addresses associated with $λ$ in the exponential parameter plane.

math.DS↗

arXiv2022

Embedding Unicritical Connectedness Loci

In this article, for degree $d\geq 1$, we construct an embedding $Φ_d $ of the connectedness locus $\mathcal{M}_{d+1}$ of the polynomials $z^{d+1}+c$ into the connectedness locus of degree $2d+1$ bicritical odd polynomials.

math.DS↗

arXiv2022

A solution to the degree-d twisted rabbit problem

We solve generalizations of Hubbard's twisted rabbit problem for analogues of the rabbit polynomial of degree $d\geq 2$. The twisted rabbit problem asks: when a certain quadratic polynomial, called the Douady Rabbit polynomial, is twisted by a cyclic subgroup of a mapping class group, to which polynomial is the resulting map equivalent (as a function of the power of the generator)? The solution to the original quadratic twisted rabbit problem, given by Bartholdi--Nekrashevych, depended on the 4-adic expansion of the power of the mapping class by which we twist. In this paper, we provide a solution that depends on the $d^2$-adic expansion of the power of the mapping class element by which we twist.

math.DS↗