Short answer: 29.2% (19/65)
Medium Answer: I only considered modern leaders (those since 1918). I started from Wikipedia’s list of elected and appointed world leaders, then removed all leaders who were either acting leaders or appointed. I also removed all leaders who did not practically hold executive power (prime minister in presidential systems, president in a parliamentary system, see details below for semi-presidential systems) or were leaders of countries with collective executives (San Marino, Switzerland). This left 65 elected world leaders, of which 19 had either a husband or father precede them as a leader of their country.
Honduras has just elected its first female president, Xiomara Castro de Zelaya, ending 12 years of rule by the National Party. She has long been a representative of the left-wing Libre Party, running for president in the 2013, 2017, and 2021 Honduran general elections. Her defeat of the fabulously corrupt Juan Orlando Hernandez will hopefully help reverse Honduras’ slide into a narco-state that has seen almost 3% of its population try to escape to the United States in 2020 alone. Of interest, Ms. Castro’s husband, Manuel “Mel” Zelaya was formerly the president from 2006-2009 until he was ousted in a coup. This of course has led to (likely overblown) accusations that Ms. Castro will simply be a front for her husband’s even more left-wing policies.
This had me wondering about which percent of elected women leaders had a male relation (either husband or father) precede them. Let me be clear that merely having a relation also be a leader by no means indicates a diminished capacity. As brief examples, consider Indira Gandhi, Benazir Bhutto, and Aang Sun Suu Kyi (before her autocratic backslide in recent years).
To dig further into this question, I perused Wikipedia’s list of elected women leaders. It quickly became clear that there would be no good way to parse this data, except to make some value judgments by hand. For obvious reasons, this list already excluded other heads of state such as monarchs. I also excluded female members of collective head-of-state bodies (Soviet Union presidiums, other Soviet Republic State Councils, San Marino, and Switzerland) and female viceregal representatives (as there are appointed). I also excluded leaders in acting capacities only and omitted leaders from states that were not widely recognized (Transnistria, Tannu Tuva). I did include states with more widespread recognition (Taiwan, Kosovo).
I then cross-referenced this list with the type of government a country has (parliamentary, presidential, or semi-presidential). For parliamentary and presidential systems, it was easy to exclude the ceremonial executive. However, there were a few states with semi-presidential systems that were a bit more of a value judgment. For Lithuania, I considered it as leaning more towards a presidential system; I considered its Baltic neighbors of Latvia and Estonia as more parliamentary. I also tried to omit leaders that were appointed – but did make some exceptions for leaders who were both elected and markedly contributed to acquiring their own leadership roles (e.g. Roza Otunbayeva of Kyrgyzstan, who was interim president in the wake of the 2010 April revolution). I also included leaders that were elected in a deputy role, but took the top spot via succession (e.g. Samia Suluhu Hassan of Tanzania, who took over after John Magufuli died of COVID-19). Finally, I tried to assess whether a country’s system of governance had changed (e.g. for Sri Lanka, Sirimavo Bandaranaike was Prime Minister when the country was a parliamentary system, even though the country is now a presidential system).
Determining whether a leader had a preceding male relative was generally quite straightforward. I did not count cases where a female elected leader had a prominent male relation that was assassinated before they held the top role (e.g. Corazon Aquino). In most cases, the relation was either a husband or a father. Two interesting cases were: the grandfather of Kaja Kallas of Estonia was also PM (but so was her father) and Chandrika Kumaratunga of Sri Lanka had both a mother and father that preceded her as leaders.
South Asia, Southeast Asia, and Latin America seemed to have particularly high rates of elected female leaders with a male relation, whereas Europe had much lower numbers. I think a future project might be to correlate these findings with the propensity of various countries to elect people from political dynasties in general (without regard to gender). Not exactly sure how to do this yet, but would appreciate any reader tips!
For some notable firsts with regards to elected women leaders:
- Khertek Anchimaa-Toka of the defunct and largley unrecognized Tuvan People’s Republic can lay some claim to being the “first elected woman head of state,” chairing her country’s presidium in 1940.
- Sirimavo Bandaranaike of Sri Lanka was the first democratically elected world leader. She was elected as prime minister in 1960. Her husband S. W. R .D. Bandaranaike, “The Silver Bell of Asia”, preceded her as prime minister from 1956 until his assassination in 1959.
- Golda Meir was the first elected female world leader without a male relation. She was prime minister of Israel from 1969 to 1974.
- Angela Merkel is the longest serving elected female world leader. She has been the German Chancellor since 2005. She will be stepping down, likely next week, after holding the top spot for an astounding 16 years.
For those interested in a full list and my rationale for including/excluding each person, please see my table here. Red indicates a world leader that doesn’t count (for reasons explained above), light green indicates a former world leader without a preceding male relation, dark green indicates a former world leader with a preceding male relation, light blue indicates a current world leader without a preceding male relation, and dark blue indicates a current world leader with a preceding male relation. I counted Ms. Castro as a current world leader (although she is technically still president-elect).
Final note: Ms. Castro’s initial campaign promises to break ties with Taiwan were worrisome, but it seems she has backed away from the temptation of autocratic money.
References
- https://en.wikipedia.org/wiki/List_of_elected_and_appointed_female_heads_of_state_and_government
- https://en.wikipedia.org/wiki/List_of_current_heads_of_state_and_government
- https://www.theguardian.com/world/2021/nov/29/xiomara-castro-declares-victory-in-honduras-presidential-election
- https://www.economist.com/the-americas/2021/12/04/honduras-looks-to-elect-its-first-female-president
- https://www.nytimes.com/2021/03/23/world/americas/honduras-juan-orlando-hernandez-drug-trial.html
- https://www.newyorker.com/magazine/2021/11/15/is-the-president-of-honduras-a-narco-trafficker
- https://www.cnn.com/2021/03/30/africa/tanzania-suspend-officials-mourning-new-president-intl/index.html
- https://www.npr.org/2021/03/17/978336051/tanzania-president-john-magufuli-a-covid-19-skeptic-has-died
- https://en.wikipedia.org/wiki/Golda_Meir
- https://www.theguardian.com/world/2021/dec/02/angela-merkel-to-bow-out-with-ceremony-live-on-german-tv
- https://www.theguardian.com/world/2021/dec/01/honduras-xiomara-castro-taiwan-china-diplomacy
Tillaux's Thoughts 
