Adding to the unpredictability, the Green Party, which wants to curb Arctic oil exploration by Norwegian companies, may well surpass the 4 percent threshold needed to enter Parliament with a larger group.
If Labor places first, it could find itself needing the Greens as a coalition partner — a potentially momentous shift given that the Greens want to phase out Norway’s oil industry, a major source of its wealth.
“It really could swing either way,” Harald Baldersheim, a professor emeritus of political science at the University of Oslo, said of the race. “From a comparative perspective,” he added, “Norwegian politics has never been — and is not — very polarized. Both blocs are gravitating toward the center. In this sense, not much is at stake.”
He added that the next government, whether led by the Conservatives or by Labor, would face pressure on Norway’s relationship with the European Union. Norway is not a member of the bloc, but — along with Iceland and Liechtenstein — it is part of the European Economic Area and the European internal market, and is governed by the same basic rules that guarantee the movement of goods, services, capital and people.
As in Britain, which historically has close ties to Norway, relations with Europe are a touchy subject, as is immigration. Norway’s population of 5.3 million is still fairly homogeneous, but is increasingly diverse.
The right-wing Progress Party is more moderate than its counterparts in Scandinavia, the far-right Sweden Democrats and the Danish People’s Party, which are largely considered outside the mainstream. Unlike those parties, the Progress Party has been part of day-to-day governance, controlling major portfolios like finance, transportation and oil.
“The four years of coalition government has tamed the Progress Party and made it harmless,” Mr. Baldersheim said.
Svein Tore Marthinsen, an independent political commentator, said that the Progress Party had prompted a more restrictive stance on migration and asylum, some tax cuts and some increased spending on infrastructure, but that the party had not carried out its promise to reduce bureaucracy.
Prime Minister Erna Solberg, 56, is likely to continue in power if her Conservative Party prevails. Her biggest opponent is Jonas Gahr Store, 57, the leader of the Labor Party, who has previously served as foreign minister and health minister, and began his career in public health.
(Mr. Gahr Store was the foreign minister in 2008 when a suicide bomber struck a luxury hotel in Kabul, Afghanistan, where he was staying, an attack that killed six people, including the Norwegian journalist Carsten Thomassen.)
Mr. Gahr Store, unusual for a Labor politician, is the heir to a fireplace-manufacturing fortune. He has been criticized in the press for investing in overseas venture capital funds that do not abide by rules as strict as those followed by the sovereign wealth fund, which is commonly called the Oil Fund. He has also faced accusations in the press of not paying full taxes on upgrades to a country home that he undertook in 2011.
Ms. Solberg has largely run a gaffe-free campaign, but has faced pressure about provocative comments made by her hard-line integration and immigration minister, Sylvi Listhaug of the Progress Party, who recently caused a furor by saying that some immigrant-heavy areas of Sweden had become “no-go zones.”
Both candidates have been active on social media. Mr. Gahr Store’s campaign posted footage of him voting on Facebook. Ms. Solberg used the platform to post a message thanking the Norwegian people “for letting me be your prime minister the last four years.”
On YouTube, as part of a campaign to stimulate youth engagement, the candidates were challenged to do impromptu sketches. (Ms. Solberg drew a school and a treasure chest to reflect her commitment to educational improvements and lower taxes; Mr. Gahr Store drew figures and a map that he said depicted his commitment to lowering climate emissions.)
A third candidate, Trygve Slagsvold Vedum, the leader of the center-right Agrarian Party, is not likely to become prime minister, but has received attention for his resistance to the government’s plan to consolidate local governments. Mr. Slagsvold Vedum also wants Norway to renegotiate its economic arrangements with the European Union. He barnstormed the country during the campaign, and handed out 10,000 cups of coffee, by his estimate, while being trailed by chefs and musicians.
Voter turnout in Norway is historically high; in the 2013 elections, it exceeded 78 percent.