Why do people like some months more than others? For many, it is all about the holidays:
“I love the scents of winter! For me, it’s all about the feeling you get when you smell pumpkin spice, cinnamon, nutmeg, gingerbread and spruce.” – Taylor Swift
while for others, it is about avoiding the cold
“A lot of people like snow. I find it to be an unnecessary freezing of water.” – Carl Reiner
and for some more disaffected souls, it is about the specifics
“August used to be a sad month for me. As the days went on, the thought of school starting weighed heavily upon my young frame.“ – Henry Rollins
Presumably all of these preferences and this angst is reflected in Ranker’s Best Months of the Year list. The graphic below provides a visualization of the opinions of ranker users. Each row is a different person, and their (sometimes incomplete) ranking of the months is shown from best-to-worst from left-to-right. The months are color coded by the four seasons: Spring has the hues of green, summer is yellow, fall has the rustic earth hues of brown, and winter is blue.
The patchwork quilt of colors and hues makes it is clear that different people have different opinions. We wanted to understand the structure of these individual differences, using cognitive data analysis.
To do this, we used a simple model of how people produce rankings—known as a Thurstonian model, going back to the 1920s in psychology—that we have previously applied successfully to Ranker data. Rather than assuming everybody’s rankings were based on a shared opinion, we allowed this version of the model to have groups or clusters of people, and for each group to have their own preferences for the months. We didn’t want to pre-determine the number of groups, and so we allowed our model to make this inference directly from the data. Our modeling approach thus involves two sorts of interacting uncertainties: about how many groups there are, and about which people belong to which group. Bayesian statistical methods are well suited to handling these sorts of uncertainties.
For fans of Bayesian cognitive graphical models — we know you’re out there — the final model we used is shown in the figure below. For non-fans of Bayesian cognitive graphical models — we KNOW you’re out there — there are three important parts. The variable gamma at the top corresponds to how many groups there are, the variables z to the side correspond to which of these groups each individual belongs, and all of this is inferred from the rankings people gave, represented by the y variables at the bottom.
The figure below shows the first key insight from the model. It shows the probability that there are 1, 2, …, 17 groups, ranging from everybody having the same opinion about the best months, to everyone having their own unique opinion. There is uncertainty about how many groups the rankings reveal, but the most likely answer is that there are four.
Assuming there are four groups, the figure below organizes the ranking data by grouping together the people most likely to belong to each group. Group 1 shows a preference for late summer and early fall, and hates cold weather. Group 2 shows a preference for the holidays. They like fall and Christmas time and despise hot weather. Group 3 loves the summertime and hates the winter. We had a look at where these people were from, and it probably comes as no surprise they’re all from the north-east of the US. The last group, a bit like Henry Rollins, stands out as a consensus of one.
This analysis shows how cognitive models with individual differences can help understand opinion groupings, and deal with difficult questions like how many groups exist. One especially interesting feature of the Best Months list is that at least one of the groups is defined more by what comes at the bottom of their lists than the top. People in group 1 don’t agree very precisely on which months they like, but they all agree they don’t like winter months. This shows that it is not just the top few items on a Ranker list that carry useful information: what comes at the bottom can be just as informative. Both what you love and hate matters.
“When I was young, I loved summer and hated winter. When I got older I loved winter and hated summer. Now that I’m even older, and wiser, I hate both summer and winter.” – Jarod Kintz
— Crystal Velasquez and Michael Lee