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<html><head><title>niplav</title>
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<p><em>author: niplav, created: 2023-11-04, modified: 2023-11-04, language: english, status: in progress, importance: 8, confidence: likely</em></p>
<blockquote>
<p><strong>Summary of a longer investigation into inconsistent preferences and
how to resolve them. I investigate two different ways of representing
inconsistent preferences, two different methods for resolving them
into consistent preferences, how these perform on seven criteria, and
how two of those criteria are incompatible. I conclude by connecting
the question to ontological crises, and offer some ideas for further
research in the area.</strong></p>
</blockquote>
<h1 id="How_to_Achieve_Coherence_and_Why_It_Matters"><a class="hanchor" href="#How_to_Achieve_Coherence_and_Why_It_Matters">How to Achieve Coherence, and Why It Matters</a></h1>
<h2 id="Introduction"><a class="hanchor" href="#Introduction">Introduction</a></h2>
<h3 id="Motivation"><a class="hanchor" href="#Motivation">Motivation</a></h3>
<h2 id="Representing_Inconsistent_Preferences"><a class="hanchor" href="#Representing_Inconsistent_Preferences">Representing Inconsistent Preferences</a></h2>
<h3 id="With_Deterministic_Options"><a class="hanchor" href="#With_Deterministic_Options">With Deterministic Options</a></h3>
<h3 id="With_Lotteries"><a class="hanchor" href="#With_Lotteries">With Lotteries</a></h3>
<h2 id="Algorithms_for_Resolution"><a class="hanchor" href="#Algorithms_for_Resolution">Algorithms for Resolution</a></h2>
<h3 id="Minimizing_EditDistance"><a class="hanchor" href="#Minimizing_EditDistance">Minimizing Edit-Distance</a></h3>
<h3 id="Hodge_Decomposition"><a class="hanchor" href="#Hodge_Decomposition">Hodge Decomposition</a></h3>
<h2 id="Desirable_Criteria"><a class="hanchor" href="#Desirable_Criteria">Desirable Criteria</a></h2>
<h3 id="Preserving_Global_Structure"><a class="hanchor" href="#Preserving_Global_Structure">Preserving Global Structure</a></h3>
<h3 id="Preserving_Local_Structure"><a class="hanchor" href="#Preserving_Local_Structure">Preserving Local Structure</a></h3>
<h3 id="Efficient_Computation"><a class="hanchor" href="#Efficient_Computation">Efficient Computation</a></h3>
<h2 id="Two_Impossibility_Theorems_with_Two_Interpretations"><a class="hanchor" href="#Two_Impossibility_Theorems_with_Two_Interpretations">Two Impossibility Theorems, with Two Interpretations</a></h2>
<h2 id="Relation_to_Ontological_Crises"><a class="hanchor" href="#Relation_to_Ontological_Crises">Relation to Ontological Crises</a></h2>
<h2 id="Summary"><a class="hanchor" href="#Summary">Summary</a></h2>
<h2 id="Further_Ideas"><a class="hanchor" href="#Further_Ideas">Further Ideas</a></h2>
</body></html>