There is St Lucy's Day (also known as Lucia) which is celebrated during December 13th.
However, the Saint Lucia hat is awarded for voting on December 15th.
Since there's no exact match, why is the hat called with this name?
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I wanted to include the symbol of light overcoming darkness as the first hat that many people receive. I knew that Santa Lucia was officially celebrated on December 13, but I had to look it up. In my experience celebrations occur in the general timeframe of the solstice, so my note on the date was "close enough".