Path Dependence

A path-dependent explanation can usually be decomposed into two causal components: (1) an original cause and (2) a maintenance structure. More contemporary formulations refer to this same distinction in terms of “critical junctures” and “mechanisms of reproduction.”

The first is the particular circumstances which caused a tradition to be started. The second is the general process by which social patterns reproduce themselves.

Stinchcombe (1968, pp. 102–3)

Some initial event or process generates a particular outcome, which is then reproduced through time even though the original generating event or process does not recur.

Pierson (2011, p. 45)

According to Pierson (2011), path-dependent (or self-reinforcing) processes share at least four defining features:

1. Multiple equilibria. Under a set of initial conditions conducive to positive feedback, a range of outcomes is generally possible.
2. Contingency. Relatively small events, if occurring at the right moment, can have large and enduring consequences.
3. A critical role for timing and sequencing. In these path-dependent processes, when an event occurs may be crucial. Because early parts of a sequence matter much more than later parts, an event that happens “too late” may have no effect, although it might have been of great consequence if the timing had been different.
4. Inertia. Once such a process has been established, positive feedback will generally lead to a single equilibrium. This equilibrium will in turn be resistant to change.

Pierson (2011, p. 44)

The preferred metaphor is that of a Polya urn process.

Here’s some R code:

library(tidyverse)
theme_set(theme_light(base_family = "Avenir Next Condensed"))

urn_process <- function(N) {
  out <- purrr::accumulate(.init = 0:1, .x = 2:N, .f = \(u, ...) {
    ## draw random sample
    draw <- sample(u, size = 1)   
    ## add draw to urn
    c(u, draw)                    
  })
  ## calculate prop at each time step
  purrr::map_dbl(out, mean)
}

Imagine a very large urn containing two balls, one black, one red. You remove one ball, and then return it to the urn along with an additional ball of the same color. You repeat this process until the urn fills up. What can we say about the eventual distribution of colored balls in the urn? Or about a series of trials in which we fill the urn and then start over again one hundred times?

Pierson (2011, p. 17)

And here is how 15 independent processes could look like:

R <- 15

M <- replicate(R, urn_process(500), simplify = FALSE)
names(M) <- 1:R

d <- as_tibble(M) |> 
  rowid_to_column(var = ".id") |> 
  pivot_longer(!.id, names_to = "path", values_to = "prop")

d |> 
  ggplot(aes(.id, prop, group = path, color = path)) + 
  geom_line(linewidth = 1/3, show.legend = FALSE) + 
  scale_y_continuous(labels = scales::percent) + 
  coord_cartesian(ylim = c(0, 1))  +
  scale_color_grey() +
  labs(
    x = "Trial Number", 
    y = "Percent of red balls in the urn", 
    title = str_glue("{R} Independent Polya Urn Processes")
  )

The first few trials correspond to a “critical juncture” and the eventual equilibrium is explained by the sampling procedure in place.

References

Pierson, Paul. 2011. Politics in Time. Princeton University Press.

Stinchcombe, Arthur L. 1968. Constructing Social Theories. University of Chicago Press.