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Denmark occupied the Island of Gotland in the Scanian War after having lost Gotland in 1645, regaining it was never a war goal. But at the end of the war Denmark occupied it plus Bremen-Verden and post-1721 Swedish Pommerania and the Duchy of Gottorp. The French forced the Danes to leave it, but France did throw the Danes a bone by recognise future Danish claims to Schleswig-Gottorp. So what if the French for some reason had decided to throw a slightly bigger bone to the Danes by letting the Swedes lose Gotland. Maybe the Swedish diplomats overplay their cards, so the French decides to teach them a lesson.

(warning I'm making a butterfly genocide)

The island are absolute not on the wish list of Denmark, but at least it makes it a symbolic victory of Denmark. The Swedes likely want it back in future wars, but beside regaining it in the early Great Northern War, Denmark would retake it. The next opportunity will be 1814, but the diplomatic cost-benefits of it, make it really not worth it. Which means that Denmark continue to keep it. It won't be lost in the Schleswigian Wars either.

Denmark was historical ahead of Sweden in agriculture, but the spread of agriculture advances build until 1800 on large estate forcing them down over their tenants. As result the selfowning farmer of Bornholm was backward compared to the tenant farmers of the rest of Denmark. Through still ahead of Scanians. I lean toward the Danish letting them be mostly self owners, but the few large estates will likely result in the spread of agriculture advances and in the 19th century Danish agricultural schools will result in the spread of know how

Population-wise Gotland had a pre-industrial population around half of pre-industrial Iceland, it have around the same size as Funen and a mostly similar climate, but slightly poorer soil. Both Gotland are relative underpopulated with only sligtly over double it pre-industrial population (60.000) compared to Funen which have 470.000 people. This could lean toward Gotland having more people under Danish rule except, Denmark also have several islands following the same patter (Bornholm, Lolland and Falster). But I lean toward the relative isolation of Gotland would lead to far smaller migration outflow to the rest of Denmark. Fundamental the bigger size of Gotland and the greater isolation from the Danish mainland would lead to a migration going to Visby instead of Copenhagen, much as we saw regional midsize cities like Odense and Aalborg keeping a relative high population density.

I doubt we will see a Funen-size population. instead I expect a population of 150-250.000. A interesting question would be whether Danish rule would result in Gotlanders becoming Danes or if we see a local national awakening as we saw in the Faroes Islands. I expect that Gutnish would survive better, but we will likely see aa similar process where it grow nearer Danish. I lean toward the Gotlanders wouldn't have a regional national awakening, as they're less isolated from Denmark than the Faroese are.

If WWII happens as in OTL Gotland will ease the evacuation of refugees and likely rsult in more people being evacuated from the Courland enclave. But afterward it will be likely occupied by USSR[1], it will likelyu be delivered back to Denmark (the reasons for USSR to deliver Bornholm back would also go for Gotland).

Under the Cold War Gotland would be NATO's eastermost outpost in the Baltic.

Denmark would likely also have a closer relationship with Latvia and Estonia as a neighbour (it should be said that the relationship are already close)

[1] there's a small chance that the greater strategic importance of Gotland to Sweden and the bigger population of Gotland would result in some of the Danish Brigade (a Danish refugee military unit in Sweden) being landed in Visby with Swedish support and the Germans surrendering to them before the Soviets could arrive. This could be interesting as a large number of Baltic refugees would not be deported back to USSR in that case.
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