The saved example contains thirteen thousand four hundred seventy-two votes across three labels: forty-five hundred, sixty-two hundred, and twenty-seven hundred seventy-two. The three bars show count divided by total, on one shared scale. They are about thirty-three point four, forty-six point zero, and twenty point six percent. These are supplied observations, not a claim about a real election or a representative population. The tool lets you replace the counts with a smaller hypothetical example: three, six, and zero. Nine observations give shares one third, two thirds, and zero. A symmetric prior of strength three adds one pseudo-count to each category. The posterior concentrations become four, seven, and one, with total twelve. The blue bar shortens from six ninths to seven twelfths, while the purple bar grows from zero to one twelfth. This is the actual pull toward equal shares. Pseudo-counts express an assumption; they are not additional surveyed people. A future poll is a second layer of uncertainty. The source first draws a probability vector from that Dirichlet posterior, then draws category counts from a multinomial poll. A seed reproduces the chosen simulated poll. A sample of five thousand has counts summing to five thousand, not to the original thirteen thousand four hundred seventy-two. Run the native simulation and download its CSV to inspect those two levels. Credible intervals summarize the model assumptions; they are not guarantees about future respondents.