Laws and institutions shape individual outcomes through complex interactions with citizens' diverse circumstances, yet how different voting methods navigate this coupled landscape remains poorly understood. We model collective governance as optimization on NK fitness landscapes, where shared bits (laws) are updated by voting while individual bits (personal traits) remain fixed. A cross-dependency parameter $α$ controls how legislation's effects depend on individual circumstances. We compare eight standard voting methods and a generalized scoring family across landscape ruggedness $K \in \{1,\ldots,20\}$ and $α\in [0,1]$ with 1000 runs per configuration. Under direct democracy, the optimal voting method undergoes sharp phase transitions as a function of landscape complexity: cardinal score voting dominates on smooth landscapes, ordinal scoring with $p=0.35$ at low-to-moderate ruggedness, Borda count across a wide middle range, and STAR voting at the highest complexity. A two-parameter empirical formula reduces the $(K, α)$ plane to a single complexity axis for visualization. Borda count achieves the highest mean fitness and lowest variance across most of the parameter space. We further introduce a representative democracy model parameterized by identity weight $β$ and candidate self-interest $p_{\mathrm{self}}$. Representation reshapes the complexity-dependent structure even under favorable conditions: cardinal score voting dominates across most regimes, with plurality emerging as the top method at high $β$ and low-to-moderate $p_{\mathrm{self}}$.

翻译：法律和制度通过与公民多样化处境的复杂互动塑造个体结果，然而不同投票方法如何驾驭这种耦合景观仍鲜为人知。我们将集体治理建模为NK适应性地貌上的优化过程，其中共享位（法律）通过投票更新，而个体位（个人特质）保持固定。一个交叉依赖参数$α$控制立法效果对个人处境的依赖程度。我们比较了八种标准投票方法和一个广义评分族，在地貌崎岖度$K\in \{1,\ldots,20\}$和$α\in [0,1]$范围内对每种配置进行1000次运行。在直接民主下，最优投票方法随景观复杂性发生急剧相变：基数评分投票在平滑地貌上占优，序数评分法在低到中等崎岖度时取$p=0.35$，博达计数法在广泛的中等范围内表现最佳，而STAR投票在最高复杂度时胜出。一个双参数经验公式将$(K, α)$平面简化为单一复杂性轴以便可视化。博达计数法在参数空间大部分区域实现最高平均适应度和最低方差。我们进一步引入由身份权重$β$和候选人自利性$p_{\mathrm{self}}$参数化的代议制民主模型。即使在有利条件下，代表性也会重塑复杂度依赖的结构：基数评分投票在大多数机制中占优，而简单多数制在$β$高且$p_{\mathrm{self}}$低至中等时成为最优方法。