Many--or perhaps all--long-distance assimilatory and dissimilatory phonological processes produce lexical or free variation exhibiting a broad generalization: the likelihood of process application decreases as the transparent distance between the trigger and the target increases (a phenomenon that I call distance-based decay). This thesis provides a unified analysis of distance-based decay, drawing from thousands of data reflecting three long-distance phonological processes across four languages. I account for the data within the framework of Maximum Entropy Harmonic Grammar (Smolensky 1986, Goldwater and Johnson 2003, Hayes and Wilson 2008), which allows for an adequate treatment of variation. I argue that distance- based decay can be captured across the four surveyed languages by an invariant decay function--a simple negative power function--that interacts with two language-specific parameters: the weight of the AGREE (for assimilatory cases) or DISAGREE (for dissimilatory cases) constraint and the weight of IDENT. My account is therefore an extension of Kimper 2011, who posits a scaling factor that scales the weight of markedness to account for the decay effect present in vowel harmony in Hungarian. While it is the case that decay rates differ across the languages I survey, my analysis accounts for such differences purely with the weights of markedness and faithfulness; that is, I show that differences in decay rate can be modeled without having to posit language-specific decay functions.

Traditional theories of phonological variation propose that morphemes be encoded with descriptors such as [+/- Rule X], to capture which of them participate in a variable process. More recent theories predict that morphemes can have LEXICAL PROPENSITIES: idiosyncratic, gradient rates at which they participate in a process—e.g., [0.7 Rule X]. This dissertation argues that such propensities exist, and that a binary distinction is not rich enough to characterize participation in variable processes. Corpus investigations into Slovenian palatalization and French liaison reveal that individual morphemes pattern across an entire propensity spectrum, and that encoding individual morphemes with gradient status improves model performance. Furthermore, an experimental investigation into French speakers’ intuitions suggests that they internalize word- specific propensities to undergo liaison. The dissertation turns to modeling language learners’ ability to acquire the idiosyncratic behavior of individual attested morphemes while frequency matching to statistical generalizations across the lexicon. A recent model based in Maximum Entropy Harmonic Grammar (MaxEnt) makes use of general constraints that putatively capture statistical generalizations across the lexicon, as well as lexical constraints governing the behavior of individual words. A series of learning simulations reveals that the approach fails to learn statistical generalizations across the lexicon: lexical constraints are so powerful that the learner comes to acquire the behavior of each attested form using only these constraints, at which point the general constraint is rendered ineffective. A GENERALITY BIAS is therefore attributed to learners, whereby they privilege general constraints over lexical ones. It is argued that MaxEnt fails to represent this property in its current formulation, and that it be replaced with the hierarchical MIXED-EFFECTS LOGISTIC REGRESSION MODEL (MIXED-EFFECTS MAXENT), which is shown to succeed in learning both a frequency-matching grammar and lexical propensities, by encoding general constraints as fixed effects and lexical constraints as a random effect. The learner treats the grammar and lexicon differently, in that vocabulary effects are subordinated to broad, grammatical effects in the learning process.