Related Party Transactions, Revenue from Transactions with Related Parties (Details) - USD ($)	3 Months Ended		9 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2023	Sep. 30, 2022	Dec. 31, 2022
Related Party Transaction [Abstract]
Investment income	$ 24,134	$ 15,545	$ 87,443	$ 29,758
Commission revenue	462,365	389,823	1,366,010	1,343,225
Gabelli Funds, LLC [Member]
Related Party Transaction [Abstract]
Affiliated investments	1,270,618		1,270,618		$ 2,259,801
Investment income	$ 18,133	$ 10,668	$ 67,628	$ 14,089
Investment, Type [Extensible Enumeration]	mghl:USTreasuryMoneyMarketFundMember	mghl:USTreasuryMoneyMarketFundMember	mghl:USTreasuryMoneyMarketFundMember	mghl:USTreasuryMoneyMarketFundMember	mghl:USTreasuryMoneyMarketFundMember
Affiliated Entities [Member] | Commissions [Member]
Related Party Transaction [Abstract]
Commission revenue	$ 325,036	$ 248,012	$ 930,455	$ 785,432
Revenue percentage	70.00%	64.00%	68.00%	58.00%