More (TODO)

Arrow’s Theorem and Measure Theory: #

“The problem of finding good voting systems has been studied at great length. For example, a quick browse reveals a bunch of impossibility theorems related to Arrow’s: the Gibbard–Satterthwaite Theorem, the Duggan–Schwartz Theorem, the Holmström Theorem, … . I know nothing about all this. But perhaps there’s something to be gained by thinking about means of structures.” + a few links there, e.g.:

Phillips Machine #

Not politcs - economics, and fun: Phillips Machine

“The society is wise precisely when even the most influential individual’s influence vanishes in the large society limit”

Opinion dynamics & information aggregation (DeGroot etc.) #

  • DeGroot consensus (a.k.a. French–DeGroot). Agents iteratively average neighbors’ opinions: @@x_{t+1}=W x_t@@ with row-stochastic @@W@@. If @@W@@ is primitive (strongly connected + aperiodic), opinions converge to consensus @@ \alpha^\top x_0@@, where @@\alpha@@ is the left eigenvector of @@W@@ (agents’ long-run “influence”). Classic baseline. ( tandfonline.com) Antecedent: French (1956) on social power. ( Communication Cache)

  • Friedkin–Johnsen (stubborn/anchored agents). DeGroot with partial stubbornness (agents keep a weight on their initial view) ⇒ persistent disagreement/partial consensus rather than full consensus; predicts polarization under certain network/anchor patterns. ( SIU Computer Science)

  • Persuasion bias (DeMarzo–Vayanos–Zwiebel). Naïve updaters double-count correlated info; network centrality (not just accuracy) drives influence; multi-issue opinions can collapse into a one-dimensional “party line.” ( LSE Personal Web Pages, Oxford Academic)

  • Naïve learning & the wisdom of crowds (Golub–Jackson). With independent private signals and DeGroot-style updating, society learns the truth iff the most influential node’s share → 0 as the network grows (no “opinion monopolies”). ( American Economic Association)

  • Bounded-confidence dynamics (Hegselmann–Krause). Nonlinear cousin: agents only average within an “opinion neighborhood.” Explains fragmentation vs. consensus depending on confidence radius and initial distribution. ( jasss.org)