The Georgist Engine
Mathematical Autopsy of Elizabeth Magie's Anti-Monopoly System
Permanent Identifier: https://doi.org/10.5281/zenodo.1089201
Scholarly Abstract
This monograph presents a formal computational and mathematical autopsy of Elizabeth Magie's 1904 Landlord's Game. By contrasting Magie's dual-ruleset architecture—the Single Tax cooperative commonwealth vs. the Monopolist elimination variant—we prove via discrete Markov chain simulations that commercial Monopoly was designed precisely as an intellectual critique of unconstrained private land rent, not a celebration of capitalist acquisition.
1. The 1904 Patent & The Dual-Ruleset Architecture
On January 5, 1904, Elizabeth J. Magie received U.S. Patent No. 748,626 for 'The Landlord's Game'. Unlike the modern commercial product published by Parker Brothers in 1935, Magie's patent encoded two distinct, competing rule systems within the exact same board topology. Under the 'Monopolist' ruleset, all rents flowed to individual private titleholders, inevitably concentrating capital until all players but one were eliminated. Under the 'Single Tax' ruleset, land rents were paid into a common Public Treasury, which funded public utilities, transport infrastructure, and universal basic dividends.
2. Markov Matrix of Board Movement & Rent Escalation
Because movement is governed by the sum of two independent six-sided dice, the probability mass function follows a triangular distribution centered at 7. The board state transitions can be represented as a 40-state ergodic Markov chain with an absorbing 'In Jail' state. When house upgrades are introduced, rent escalates non-linearly, scaling from $50 on base monopolies to $1,050+ on hotels.
P(X = k) = \frac{6 - |k - 7|}{36} \quad \text{for } k \in \{2, \dots, 12\}\mathbf{S}_{t+1} = \mathbf{S}_t \mathbf{P}, \quad \lim_{t \to \infty} \mathbf{S}_t = \mathbf{\pi}3. Simulating the Casual House Rule Pathology
Our Monte Carlo simulations demonstrate that common casual house rules—specifically injecting tax fines into Free Parking and disabling mandatory property auctions—distort the game's termination probability. By subsidizing bankrupted players and preventing asset price discovery, house rules elevate expected match duration from 65 minutes to 240+ minutes, turning a sharp economic demonstration into an agonizing war of attrition.