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“重男轻女”是否会导致男女比例失衡？

· Xiebro

在一个严重受到“重男轻女”思想影响的村庄里，父母渴望拥有男孩，因此每当生下女孩时，他们就会不断地生育，直到有一天生下男孩为止。由于计划生育政策的限制，一旦有了男孩，就不能再生了。

那么，在这个村庄里的男女比例应该是怎样的？是否会偏向男性？

我们可以通过使用蒙特卡洛方法来模拟现实场景，计算出该村庄的男女比例。

simulate_once <- function(N, prob = 0.5, verbose = FALSE) {
    
    # nobody has anything yet...
    boys  = 0; girls = 0;
    
    print_vars <- function() {
        message("Boy-to-Girl Ratio: ", boys, " / ", girls)
        message("====================================")
    }
    
    tryonemore <- function(x, msgON) {
        
        if(msgON) message(x)
        
        # terminal condition: all 1 (boys)
        if (all(x)) {
            boys  <<- boys + sum(x)
            if (msgON) print_vars()
            return(1)
        }
        
        # assign to parent env so that we can keep track
        boys  <<-  boys + sum(x)
        girls <<- girls + sum(!x)
        
        if (msgON) print_vars()
        return(tryonemore(rbinom(sum(!x), 1, prob), msgON = msgON))
    }
    
    # initial call
    tryonemore(rbinom(N, 1, prob), msgON = verbose)
    return(boys / girls)
}

假设村庄里有10个家庭，我们先来尝试进行一次模拟：

set.seed(1111)
simulate_once(N = 10, verbose = TRUE)
# # 0010111010
# # Boy-to-Girl Ratio: 5 / 5
# # ====================================
# # 01111
# # Boy-to-Girl Ratio: 9 / 6
# # ====================================
# # 0
# # Boy-to-Girl Ratio: 9 / 7
# # ====================================
# # 1
# # Boy-to-Girl Ratio: 10 / 7
# # ====================================
# # [1] 1.428571

从模拟结果来看，男10/女7=1.428571比例似乎失衡了，但这只是对拥有10个家庭规模的小村庄进行了一次模拟的观测结果，那么，如果对不同规模的村庄分别进行足够多次的模拟，答案是否会有不同？

  • 分别模拟10~2000个家庭规模的村庄；
  • 分别对每个村庄进行1000次模拟，求模拟结果的期望值
library(furrr)

# for paralle computing
plan(multisession, workers = 10)

# simulate from small village to large village
village_size = 10:2000

# for every single village we simulate 1000 times
simulate_many <- function(N, trials = 1000) {
    replicate(trials, simulate_once(N, verbose = FALSE))
}

# start simulation
res <- furrr::future_map_dbl(village_size, ~ mean(simulate_many(.x)))

library(ggplot2)

p <- 
  cbind(size = village_size, ev = res) |>
  as.data.frame() |>
  ggplot(aes(size, ev)) + 
  geom_line(alpha = 0.7) + 
  geom_hline(yintercept = 1, col = "red", lty = 4) +
  theme_minimal(base_family = "Osaka") + 
  labs(x = "Village Size", y = "", title = "Expected Value of Boy-Girl Ratio")

p

# zoom in
p + coord_cartesian(ylim = c(0.9, 1.05))

从上图结果来看，当村庄达到一定规模后(约1000个家庭)，即使“重男轻女”也不会导致男女比例的失衡。