The thermometer

“Please rate each party on a scale from 0 to 100. Ratings above 50 mean you feel warm toward it, below 50 cold.”

\[ AP_i = T_{i,\text{in}} - T_{i,\text{out}} = 85 - 20 = 65 \tag{1}\]

From one person to a country

Who is in?

Equation 1 needs an in-party before it can be computed. Who decides which party is the respondent’s own?

• Attachment: the party they say they feel close to
• Vote choice: the party they voted for
• Most liked: the party they rate highest

Even with two parties, there is a conceptual choice before the arithmetic starts.

The problem

• With many parties there is no single “other party” to subtract
• People can like more than one party, and form blocs (Wagner 2021)
• Dislike can grow without a strong in-party, for example toward a new radical party
• Parties differ in size

Each measure answers these questions differently.

One respondent, four parties

Figure 2: A fictional respondent rates four parties on the 0 to 10 like/dislike scale: A 10, B 9, C 4, D 1. Vote shares in brackets. The same ratings feed every measure on the following slides.

• The respondent feels close to Party A
• Vote shares follow Wagner (2021), Table 1

Reiljan: the AP index

Unweighted: \(10 - \frac{9+4+1}{3} = 10 - 4.67 = \mathbf{5.33}\)

\[ AP_n = \sum_{m \neq n} (\text{Like}_n - \text{Like}_m) \frac{V_m}{1 - V_n} \tag{3}\]

\[ API = \sum_{n} AP_n \times V_n \tag{4}\]

\(n\) is the in-party, \(m\) an out-party, \(V\) a vote share.

• In-group: the party you feel close to
• Only partisans get a score
• One in-group: B counts as an out-party

Wagner: mean distance

Unweighted: \(\sqrt{\frac{1+36+81}{3}} = \sqrt{39.3} = \mathbf{6.27}\)

\[ \text{Distance}_i = \sqrt{\frac{\sum_{p} (\text{like}_{ip} - \text{like}_{\max,i})^2}{n_p}} \tag{5}\]

\[ \text{Distance}^{w}_i = \sqrt{\sum_{p} v_p (\text{like}_{ip} - \text{like}_{\max,i})^2} \tag{6}\]

\(n_p\) counts the parties other than the most-liked one, \(v_p\) is a vote share.

• In-group: the party you rate highest
• Anyone with two ratings gets a score
• Squaring stresses the most disliked party

Wagner: spread of scores

Unweighted: \(\sqrt{\frac{16+9+4+25}{4}} = \sqrt{13.5} = \mathbf{3.67}\)

\[ \text{Spread}_i = \sqrt{\frac{\sum_{p} (\text{like}_{ip} - \overline{\text{like}}_i)^2}{n_p}} \tag{7}\]

\[ \text{Spread}^{w}_i = \sqrt{\sum_{p} v_p (\text{like}_{ip} - \overline{\text{like}}_i)^2} \tag{8}\]

\[ \overline{\text{like}}_i = \sum_{p} v_p \, \text{like}_{ip} \tag{9}\]

• No in-group at all
• Everyone with two ratings gets a score
• Allows blocs: two liked parties against two disliked ones

Why weight?

The scale shows every party as an equal line, but parties are not equal in size.

• For: disliking a 40% party says more about a system than disliking a 3% one (Wagner 2021)
• For: surveys list different numbers of small parties, and weights damp that
• Against: more choices to make and report
• Against: AP changes when vote shares change, even if no feeling changes (Reiljan 2020)

Same ratings, three scores

Does the choice matter?

• Levels differ: distance always sits above spread
• Rankings barely move: the measures correlate at about .9
• Few voters have one strong in-party
• The US is average in this comparison

Check the robustness of your result across measures, and report it.

Population of inference

Do we want the AP of

• partisans (attached to a party)?

• voters (voted for one)?

• partisans and voters?

• the whole sample?

• The answer fixes how the in-group is coded

• And it fixes whose AP the estimate describes

• API: partisans only. Distance and spread: anyone who rates two parties.

Who is in the sample?

Say whose AP

• A partisans-only estimate in Latvia describes about a third of respondents, in Denmark about four in five
• A difference between them may be a difference in who was counted

Back to the definition

“the tendency of people identifying as [partisans] to view opposing partisans negatively and copartisans positively” (Iyengar and Westwood 2015, 691)

• The definition is about people: fellow citizens who support a party
• The standard thermometer asks about parties
• Thermometers can also target partisans, for example “Democratic Party voters” (Druckman and Levendusky 2019)
• Whom do respondents picture: the neighbour, or the party leader? (Druckman and Levendusky 2019)

D&L (2019): design

1. Do the measures agree? Thermometer, trait ratings, trust, social distance
2. Whom do people picture? Random assignment of the target:
   • “the Democratic (Republican) Party”
   • “Democratic (Republican) Party voters”
   • “Democratic (Republican) Party candidates and elected officials”

US online survey, 2017, partisans and leaners, N about 2,200

D&L (2019): results

• “The party” means its elites
• People dislike out-party voters, and out-party elites even more
• Thermometer, traits and trust correlate well, social distance much less

Vertical and horizontal

• Vertical AP: affect toward parties and their elites

• Horizontal AP: affect toward ordinary citizens who support them (Areal and Harteveld 2024)

• The definition is horizontal

• A party thermometer is vertical, a thermometer of party voters is horizontal

• They are related, but not the same thing

Where do our measures sit?

Place today’s measures and last week’s in the grid.

The grid filled in

Today: the left column. Next week: the bottom right.

Recap: takeaways

• In two-party systems, AP is the in-party minus the out-party rating, averaged over any group
• In multiparty systems, API, distance and spread give different numbers from the same ratings
• Each measure assumes who the in-group is, and who gets a score
• That choice fixes whose AP an estimate describes
• Party thermometers capture vertical AP, mostly feelings about elites

Recap: learning goals

Goal 1. What a thermometer measures

• Warmth toward parties, which respondents read as their elites, not toward fellow partisans

Goal 2. Building an AP score with many parties

• Pick an in-group rule (closeness, top rating, none), a distance (plain or squared), and weights (or none)

Goal 3. Who counts as a partisan

• The in-group rule decides who gets a score, so it decides whose AP you estimate

Goal 4. Comparisons across countries and time

• Only with the same measure, and with the sample composition reported

Start now

• Begin thinking about what interests you, and look for data and papers
• A good strategy: take an existing empirical paper that interests you, and tweak it
  • another country, period, measure, population or outcome
• That is completely fine, and it is how much published research starts

What I expect

A paper as close to publication-ready as possible. Above all, I care about the logic of the argument.

The magic five:

1. Introduction
2. Theory
3. Research design
4. Empirical analysis
5. Conclusion

• The whole paper is one large argument
• Every section, and every paragraph, is a smaller argument that serves it

Sections as arguments (1)

Introduction: why your research question is interesting (puzzling), or important, or both. Then a short overview of all other sections.

Theory: why, based on the literature and your own reasoning, things should be the way you expect. Ideally: why your hypotheses follow logically from the state of research.

Research design: why your data, measurement and analysis are well suited to the question and the hypotheses. Be open about what the data can and cannot do. Do not overclaim.

Sections as arguments (2)

Empirical analysis: why the patterns in your results support, or contradict, your hypotheses and interpretations. Again, be honest about what the method can and cannot say.

Conclusion: a recap of the whole chain of argument, and why your study contributes to the literature.