Search versus Search for Collapsing Electoral Control Types

Electoral control types are ways of trying to change the outcome of elections by altering aspects of their composition and structure [BTT92]. We say two compatible (i.e., having the same input types) control types that are about the same election system E form a collapsing pair if for every possible input (which typically consists of a candidate set, a vote set, a focus candidate, and sometimes other parameters related to the nature of the attempted alteration), either both or neither of the attempted attacks can be successfully carried out [HHM20]. For each of the seven general (i.e., holding for all election systems) electoral control type collapsing pairs found by Hemaspaandra, Hemaspaandra, and Menton [HHM20] and for each of the additional electoral control type collapsing pairs of Carleton et al. [CCH+ 22] for veto and approval (and many other election systems in light of that paper's Theorems 3.6 and 3.9), both members of the collapsing pair have the same complexity since as sets they are the same set. However, having the same complexity (as sets) is not enough to guarantee that as search problems they have the same complexity. In this paper, we explore the relationships between the search versions of collapsing pairs. For each of the collapsing pairs of Hemaspaandra, Hemaspaandra, and Menton [HHM20] and Carleton et al. [CCH+ 22], we prove that the pair's members' search-version complexities are polynomially related (given access, for cases when the winner problem itself is not in polynomial time, to an oracle for the winner problem). Beyond that, we give efficient reductions that from a solution to one compute a solution to the other. For the concrete systems plurality, veto, and approval, we completely determine which of their (due to our results) polynomially-related collapsing search-problem pairs are polynomial-time computable and which are NP-hard.Comment: The metadata's abstract is abridged due to arXiv.org's abstract-length limit. The paper itself has the unabridged (i.e., full) abstrac

Separating and Collapsing Electoral Control Types

[HHM20] discovered, for 7 pairs (C,D) of seemingly distinct standard electoral control types, that C and D are identical: For each input I and each election system, I is a Yes instance of both C and D, or of neither. Surprisingly this had gone undetected, even as the field was score-carding how many std. control types election systems were resistant to; various "different" cells on such score cards were, unknowingly, duplicate effort on the same issue. This naturally raises the worry that other pairs of control types are also identical, and so work still is being needlessly duplicated. We determine, for all std. control types, which pairs are, for elections whose votes are linear orderings of the candidates, always identical. We show that no identical control pairs exist beyond the known 7. We for 3 central election systems determine which control pairs are identical ("collapse") with respect to those systems, and we explore containment/incomparability relationships between control pairs. For approval voting, which has a different "type" for its votes, [HHM20]'s 7 collapses still hold. But we find 14 additional collapses that hold for approval voting but not for some election systems whose votes are linear orderings. We find 1 additional collapse for veto and none for plurality. We prove that each of the 3 election systems mentioned have no collapses other than those inherited from [HHM20] or added here. But we show many new containment relationships that hold between some separating control pairs, and for each separating pair of std. control types classify its separation in terms of containment (always, and strict on some inputs) or incomparability. Our work, for the general case and these 3 important election systems, clarifies the landscape of the 44 std. control types, for each pair collapsing or separating them, and also providing finer-grained information on the separations.Comment: The arXiv.org metadata abstract is an abridged version; please see the paper for the full abstrac

Socio-Economic and Governance Conditions Corresponding to Change in Animal Agriculture: South Dakota Case Study

Understanding sustainable livestock production requires consideration of both qualitative and quantitative factors in a temporal and/or spatial frame. This study adapted Qualitative Comparative Analysis (QCA) to relate conditions of social, economic, and governance factors to changes in livestock inventory across several counties and over time. This paper presents an approach that (1) identified factors with the potential to relate to a change in livestock inventory and (2) analyzed commonalities within these factors related to changes spatially and temporally. This paper illustrates the approach and results when applied to five counties in eastern South Dakota. The specific response variables were periods of increasing, no change, or decreasing beef cattle, dairy cattle, and swine inventories in the specific counties for five-year census periods between 1992 and 2017. In the spatial analysis of counties, stable beef inventories and decreasing dairy inventories related to counties with increasing gross domestic products. The presence of specific social communities related to increases in county swine inventories. In the temporal analysis of census periods, local governance and economic factors, particularly market price influences, were more prevalent. Swine inventory showed a stronger link to cash crop markets than to livestock markets, whereas cattle market price increases associated with stable inventories for all animal types. Local governance tools had mixed effects for the different animal types across space and time. The factors and analysis results are context-specific. However, the process considers the various socio-economic processes in livestock production and community development applicable to agricultural sustainability questions in the Midwest and beyond

Socio-Economic and Governance Conditions Corresponding to Change in Animal Agriculture: South Dakota Case Study

Understanding sustainable livestock production requires consideration of both qualitative and quantitative factors in a temporal and/or spatial frame. This study adapted Qualitative Comparative Analysis (QCA) to relate conditions of social, economic, and governance factors to changes in livestock inventory across several counties and over time. This paper presents an approach that (1) identified factors with the potential to relate to a change in livestock inventory and (2) analyzed commonalities within these factors related to changes spatially and temporally. This paper illustrates the approach and results when applied to five counties in eastern South Dakota. The specific response variables were periods of increasing, no change, or decreasing beef cattle, dairy cattle, and swine inventories in the specific counties for five-year census periods between 1992 and 2017. In the spatial analysis of counties, stable beef inventories and decreasing dairy inventories related to counties with increasing gross domestic products. The presence of specific social communities related to increases in county swine inventories. In the temporal analysis of census periods, local governance and economic factors, particularly market price influences, were more prevalent. Swine inventory showed a stronger link to cash crop markets than to livestock markets, whereas cattle market price increases associated with stable inventories for all animal types. Local governance tools had mixed effects for the different animal types across space and time. The factors and analysis results are context-specific. However, the process considers the various socio-economic processes in livestock production and community development applicable to agricultural sustainability questions in the Midwest and beyond.This article is published as Welles, Jacqueline S., Noelle Cielito T. Soriano, Freda Elikem Dorbu, G. M. Pereira, Laura M. Rubeck, Erica L. Timmermans, Benjamin Ndayambaje et al. "Socio-Economic and Governance Conditions Corresponding to Change in Animal Agriculture: South Dakota Case Study." Sustainability 13, no. 19 (2021): 10682. DOI: 10.3390/su131910682. Copyright 2021 by the authors. Attribution 4.0 International (CC BY 4.0). Posted with permission