Total Result¶
The SimulationTotalResult class aggregates multiple SimulationSeriesResult instances across a parameter space defined by three axes:
- Generative model (e.g.
UNI,IC,VMF_HC) - Number of voters (e.g.
11,101,1001) - Number of candidates (e.g.
3,14)
Each series is uniquely keyed by its (gen_model, n_voters, n_candidates) triplet.
The class enables filtering, metric pivoting, comparison plots, and persistence across the entire parameter space.
Quick start¶
From a TOML config (recommended)¶
The simplest way to build a SimulationTotalResult is via simulation_series_from_config, which iterates over every combination defined in your config file:
from vote_simulation.simulation.simulation import simulation_series_from_config
total = simulation_series_from_config("config/simulation.toml")
print(total)
# SimulationTotalResult(series=6, models=['VMF_HC'], voters=[11, 101, 1001], candidates=[3, 14])
Manual construction¶
You can also build it by hand, calling simulation_instance for each point in the parameter grid:
from vote_simulation.models.results.total_result import SimulationTotalResult
from vote_simulation.simulation.simulation import simulation_instance
rules = ["PLU1", "PLU2", "BORD", "RV", "COPE", "HARE", "MJ"]
total = SimulationTotalResult()
for model in ["UNI", "IC"]:
for n_v in [101, 1001]:
for n_c in [3, 14]:
series = simulation_instance(model, n_v, n_c, rules, n_iteration=100)
total.add_series(series)
Duplicate keys
add_series() raises ValueError if a series with the same (model, voters, candidates) key is already present.
Use replace_series() to overwrite an existing entry.
Series key¶
Each series is indexed by a SeriesKey named tuple:
from vote_simulation.models.results.total_result import SeriesKey
key = SeriesKey(gen_model="UNI", n_voters=101, n_candidates=3)
You can check membership and retrieve series by key:
Accessors¶
| Property / method | Returns | Description |
|---|---|---|
series_count |
int |
Number of stored series |
keys |
list[SeriesKey] |
Sorted list of all keys |
gen_models |
list[str] |
Distinct model codes |
voter_counts |
list[int] |
Distinct voter counts |
candidate_counts |
list[int] |
Distinct candidate counts |
get_series(model, nv, nc) |
SimulationSeriesResult |
Look up one series |
len(total) |
int |
Same as series_count |
key in total |
bool |
Membership test |
Iteration yields (SeriesKey, SimulationSeriesResult) pairs in sorted order:
for key, series in total:
print(f"{key} → {series.step_count} steps, mean_dist={series.mean_distance:.1f}%")
Filtering¶
filter() returns a new SimulationTotalResult sharing the same series objects (shallow copy).
All three parameters are optional keyword-only arguments — combine as needed:
# Keep only UNI model
uni = total.filter(gen_model="UNI")
# Keep only 14-candidate runs
c14 = total.filter(n_candidates=14)
# Combine: IC model with 3 candidates
ic3 = total.filter(gen_model="IC", n_candidates=3)
Filtering is the key step before plotting or pivoting: most methods require that the "third" parameter (the one not on the axes) has a single distinct value.
Metrics¶
Summary DataFrame¶
summary_frame() returns one row per series with scalar metrics:
Columns: gen_model, n_voters, n_candidates, step_count, n_iterations, mean_distance, most_distant_rule_a, most_distant_rule_b, most_distant_distance.
Metric matrix (pivot)¶
metric_matrix() pivots a scalar metric into a 2D table across two parameters.
The third parameter must be fixed to a single value (filter first if needed).
# Fix voters → pivot models vs candidates
pivot, desc = total.filter(n_voters=101).metric_matrix(
row_param="gen_model",
col_param="n_candidates",
metric="mean_distance",
)
print(f"Fixed: {desc}")
print(pivot)
Output:
Valid axis parameters: "gen_model", "n_voters", "n_candidates".
Rule-pair distance¶
rule_pair_frame() extracts the mean distance between two specific rules across all series:
gen_model n_voters n_candidates distance
IC 101 3 24.00
IC 101 14 72.17
UNI 101 3 24.00
UNI 101 14 72.17
Winner metrics¶
SimulationTotalResult exposes two methods to analyse winner quality metrics (see WinnerMetrics) aggregated across the entire parameter space.
Available metric fields¶
The following fields are available in every WinnerMetrics object and can be used as the metric_field argument:
| Field | Type | Description |
|---|---|---|
social_acceptability |
float |
Fraction of voters who prefer the winner(s) to every other candidate |
utility_mean |
float |
Mean cardinal utility of the co-winner(s) across all voters |
utility_median |
float |
Median cardinal utility of the co-winner(s) |
utility_var |
float |
Variance of cardinal utility of the co-winner(s) |
rank_mean |
float |
Mean Borda rank of the co-winner(s) (0 = worst, n_candidates−1 = best) |
rank_median |
float |
Median Borda rank of the co-winner(s) |
rank_var |
float |
Variance of Borda rank of the co-winner(s) |
freq_first |
float |
Fraction of voters who rank a co-winner first |
freq_last |
float |
Fraction of voters who rank a co-winner last |
has_tie |
bool |
Whether there are multiple co-winners |
n_cowinners |
int |
Number of co-winners |
metrics_comparison_frame¶
metrics_comparison_frame() returns a long-form DataFrame with one row per (gen_model, n_voters, n_candidates) entry, containing the aggregated statistic for one rule and one metric:
df = total.metrics_comparison_frame("social_acceptability", "COPE")
print(df.to_string(index=False))
gen_model n_voters n_candidates social_acceptability_mean
IC 50 3 0.71
IC 50 7 0.63
UNI 50 3 0.68
UNI 50 7 0.59
Parameters:
metric_field— one of the fields listed in the table aboverule_code— normalised rule code (e.g."COPE","AP_T0")stat—"mean"(default) or"std"
Series without the requested rule's metrics are silently omitted.
metrics_pivot¶
metrics_pivot() is the 2-D counterpart of metrics_comparison_frame(): it pivots the long-form table into a matrix, analogously to metric_matrix() for rule-distance metrics.
pivot, fixed = total.metrics_pivot(
"social_acceptability", "COPE",
row_param="n_voters",
col_param="n_candidates",
)
print(f"Fixed: {fixed}")
print(pivot.to_string())
pivot2, fixed2 = total.metrics_pivot(
"rank_mean", "AP_T0",
row_param="n_voters",
col_param="n_candidates",
)
print(f"Fixed: {fixed2}")
print(pivot2.to_string())
Parameters mirror metric_matrix():
| Parameter | Type | Description |
|---|---|---|
metric_field |
str |
Metric field name (see table above) |
rule_code |
str |
Rule to inspect |
row_param |
str |
Row axis — "gen_model", "n_voters", or "n_candidates" |
col_param |
str |
Column axis — "gen_model", "n_voters", or "n_candidates" |
stat |
str |
"mean" (default) or "std" |
Filter before pivoting
If the third parameter has more than one distinct value, metrics_pivot() averages over it implicitly. Use .filter(...) beforehand when you want a strict 2-D slice.
Plotting¶
All plot methods accept show=False to skip plt.show() and save_path to write to disk.
They return the matplotlib Axes object for further customization.
Metric heatmap¶
Visualize a scalar metric across two parameter axes:
total.filter(n_voters=101).plot_metric_heatmap(
row_param="gen_model",
col_param="n_candidates",
metric="mean_distance",
show=False,
save_path="results/metric_heatmap.png",
)
This produces a color-coded matrix where each cell shows the mean_distance for that (model, candidates) combination.
Rule-pair heatmap¶
Focus on a single pair of rules:
total.filter(n_voters=101).plot_rule_pair_heatmap(
"PLU1", "BORD",
row_param="gen_model",
col_param="n_candidates",
show=False,
save_path="results/rule_pair.png",
)
Comparison grid¶
Side-by-side full rule-distance heatmaps, one per value of a varying parameter:
total.filter(gen_model="UNI", n_voters=101).plot_comparison_grid(
"n_candidates",
show=False,
save_path="results/comparison_grid.png",
)
This is particularly useful to visually compare how rule agreement changes when the number of candidates increases, with all other variables held constant.
Filter before plotting
plot_comparison_grid requires that the two non-varying parameters are each fixed to a single value.
Chain .filter(...) before calling it.
Persistence¶
Save to directory¶
Each series is saved as a separate parquet file named after its config label:
total.save_to_dir("results/total/")
# Creates:
# results/total/UNI_v101_c3_i100.parquet
# results/total/UNI_v101_c14_i100.parquet
# ...
Load from directory¶
Delete¶
Complete example¶
from vote_simulation.models.results.total_result import SimulationTotalResult
from vote_simulation.simulation.simulation import simulation_instance
# 1) Build
rules = ["PLU1", "PLU2", "BORD", "RV", "COPE", "HARE", "MJ"]
total = SimulationTotalResult()
for model in ["UNI", "IC"]:
for n_c in [3, 14]:
series = simulation_instance(model, 101, n_c, rules, n_iteration=50)
total.add_series(series)
# 2) Explore
print(total)
print(total.summary_frame())
# 3) Filter + pivot
pivot, desc = total.filter(n_voters=101).metric_matrix(
"gen_model", "n_candidates",
)
print(pivot)
# 4) Plot
total.filter(n_voters=101).plot_metric_heatmap(
"gen_model", "n_candidates", show=False,
save_path="metric_heatmap.png",
)
total.filter(gen_model="UNI", n_voters=101).plot_comparison_grid(
"n_candidates", show=False,
save_path="comparison.png",
)
# 5) Persist
total.save_to_dir("results/total/")
loaded = SimulationTotalResult.load_from_dir("results/total/")
assert loaded.series_count == total.series_count
API reference¶
Total result model for vote_simulation.
Aggregates multiple :class:SimulationSeriesResult instances across a
parameter space defined by generative model, number of voters, and
number of candidates.
Each series is uniquely keyed by (gen_model, n_voters, n_candidates).
Provides filtering, scalar-metric pivots, and comparison plots.
Typical workflow::
total = SimulationTotalResult()
for model in ["UNI", "IC"]:
for n_v in [101, 1001]:
for n_c in [3, 14]:
series = simulation_instance(model, n_v, n_c, rules)
total.add_series(series)
# Fix model, compare across voters x candidates
uni = total.filter(gen_model="UNI")
uni.plot_metric_heatmap(row_param="n_voters", col_param="n_candidates")
# Side-by-side rule distance heatmaps varying candidates
total.filter(gen_model="UNI", n_voters=1001) \
.plot_comparison_grid("n_candidates")
SeriesKey
¶
Bases: NamedTuple
Identifies one series in the (model, voters, candidates) space.
Source code in src/vote_simulation/models/results/total_result.py
SimulationTotalResult
dataclass
¶
Collection of series results spanning a parameter space.
Each series is uniquely keyed by (gen_model, n_voters, n_candidates).
Provides filtering, scalar-metric pivots, and comparison plots.
Source code in src/vote_simulation/models/results/total_result.py
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candidate_counts
property
¶
Sorted distinct candidate counts.
gen_models
property
¶
Sorted distinct generative-model codes.
keys
property
¶
Sorted list of all series keys.
rule_codes
property
¶
Distinct rule codes available across stored series.
The order is deterministic and follows the first occurrence when iterating over series in sorted key order.
rules
property
¶
Backward-compatible alias for the distinct rule codes in the result.
series_count
property
¶
Number of stored series.
voter_counts
property
¶
Sorted distinct voter counts.
__iter__()
¶
add_series(series)
¶
Register a series result.
Raises:
| Type | Description |
|---|---|
ValueError
|
If a series with the same key is already present. |
Source code in src/vote_simulation/models/results/total_result.py
delete_dir(dir_path)
staticmethod
¶
Remove a saved total-result directory.
Returns True if the directory existed and was deleted.
Source code in src/vote_simulation/models/results/total_result.py
export_mean_distance_matrix_csv(save_path)
¶
Export :meth:mean_distance_matrix_frame to CSV.
Source code in src/vote_simulation/models/results/total_result.py
export_metrics_rules_matrix_csv(save_path, *, stat='mean', metrics=None)
¶
Export :meth:metrics_rules_matrix_frame to CSV.
Source code in src/vote_simulation/models/results/total_result.py
filter(*, gen_model=None, n_voters=None, n_candidates=None)
¶
Return a new instance containing only the matching series.
Series objects are shared (shallow copy), not deep-copied.
Source code in src/vote_simulation/models/results/total_result.py
filter_rules(rule_codes)
¶
Return a new instance where every series is restricted to rule_codes.
Applies
:meth:~vote_simulation.models.results.series_result.SimulationSeriesResult.filter_rules
to each stored series. Entries whose filtered version contains no
rules are dropped. Series keys are preserved.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
rule_codes
|
list[str]
|
Rule codes to keep across all series. Unknown or absent codes are silently ignored per series. |
required |
Returns:
| Type | Description |
|---|---|
SimulationTotalResult
|
A new :class: |
Source code in src/vote_simulation/models/results/total_result.py
get_series(gen_model, n_voters, n_candidates)
¶
Retrieve a single series by its parameter triple.
Raises:
| Type | Description |
|---|---|
KeyError
|
If no matching series exists. |
Source code in src/vote_simulation/models/results/total_result.py
load_from_dir(dir_path)
classmethod
¶
Reconstruct a :class:SimulationTotalResult from a folder of parquet files.
Each .parquet file is loaded as a :class:SimulationSeriesResult
and registered via :meth:add_series.
Source code in src/vote_simulation/models/results/total_result.py
map_rules_2d()
¶
Project rules into 2D using Multi-Dimensional Scaling (MDS).
Uses the global mean distance matrix (averaged over all series) as a precomputed dissimilarity matrix.
Returns:
| Type | Description |
|---|---|
MdsProjection
|
class: |
Raises:
| Type | Description |
|---|---|
ValueError
|
If no series have been added yet. |
Source code in src/vote_simulation/models/results/total_result.py
map_rules_3d()
¶
Project rules into 3D using Multi-Dimensional Scaling (MDS).
Uses the global mean distance matrix (averaged over all series) as a precomputed dissimilarity matrix.
Returns:
| Type | Description |
|---|---|
MdsProjection
|
class: |
Raises:
| Type | Description |
|---|---|
ValueError
|
If no series have been added yet. |
Source code in src/vote_simulation/models/results/total_result.py
mean_distance_matrix_frame()
¶
Mean rule-distance matrix averaged across all series as a DataFrame.
Source code in src/vote_simulation/models/results/total_result.py
metric_matrix(row_param='n_voters', col_param='n_candidates', *, metric='mean_distance')
¶
Pivot a scalar metric into a 2D matrix.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
row_param
|
str
|
Key field for the row axis. |
'n_voters'
|
col_param
|
str
|
Key field for the column axis. |
'n_candidates'
|
metric
|
str
|
Column name from :meth: |
'mean_distance'
|
Returns:
| Type | Description |
|---|---|
DataFrame
|
|
str
|
human-readable description of the fixed (third) parameter. |
tuple[DataFrame, str]
|
If the third parameter has multiple distinct values, they are |
tuple[DataFrame, str]
|
averaged and the description reflects this. |
Source code in src/vote_simulation/models/results/total_result.py
metrics_comparison_frame(metric_field, rule_code, stat='mean')
¶
Cross-parameter table of one winner metric for one rule.
Builds a long-form :class:~pandas.DataFrame with one row per
(gen_model, n_voters, n_candidates) entry, containing the
requested aggregated statistic for rule_code.
Parameters¶
metric_field:
One of the fields in
:data:~vote_simulation.models.rules.winner_metrics.METRIC_FIELDS
(e.g. "social_acceptability", "rank_mean").
rule_code:
The normalised rule code to extract (e.g. "COPE").
stat:
Which statistic column to read from
:attr:~vote_simulation.models.results.series_result.SimulationSeriesResult.metrics_summary_frame:
"mean" (default) or "std".
Returns¶
pd.DataFrame
Columns: gen_model, n_voters, n_candidates,
<metric_field>_<stat>. Series without the requested rule's
metrics are omitted.
Source code in src/vote_simulation/models/results/total_result.py
metrics_pivot(metric_field, rule_code, row_param='n_voters', col_param='n_candidates', stat='mean')
¶
Pivot :meth:metrics_comparison_frame into a 2D matrix.
Analogous to :meth:metric_matrix but for winner metrics instead of
rule-distance metrics.
Parameters¶
metric_field:
Metric field name (see :data:~vote_simulation.models.rules.winner_metrics.METRIC_FIELDS).
rule_code:
The rule to inspect.
row_param / col_param:
Which of the three key parameters (gen_model, n_voters,
n_candidates) to use as row/column axes.
stat:
"mean" or "std".
Returns¶
(pivot_df, fixed_description) The pivot DataFrame and a description of the fixed third parameter.
Source code in src/vote_simulation/models/results/total_result.py
metrics_rules_matrix_frame(*, stat='mean', metrics=None)
¶
Winner-metric matrix with rules as rows and metric stats as columns.
Source code in src/vote_simulation/models/results/total_result.py
plot_comparison_grid(vary_param='n_candidates', *, annotate=True, show=True, save_path=None)
¶
Side-by-side rule-distance heatmaps, one per value of vary_param.
The other two parameters must each have a single distinct value
— use :meth:filter first.
Example::
total.filter(gen_model="UNI", n_voters=1001) \
.plot_comparison_grid("n_candidates")
Source code in src/vote_simulation/models/results/total_result.py
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plot_mean_distance_matrix(ax=None, *, annotate=True, show=True, save_path=None)
¶
Heatmap of the mean rule-distance matrix averaged across all series.
Each cell (i, j) shows the average percentage of iterations where
rules i and j disagreed, averaged over every series currently in
the object. Use :meth:filter to restrict the scope first.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
ax
|
Any | None
|
Optional matplotlib Axes. A new figure is created when None. |
None
|
annotate
|
bool
|
Whether to print cell values on the heatmap. |
True
|
show
|
bool
|
Whether to call |
True
|
save_path
|
str | None
|
Optional file path to save the figure. |
None
|
Returns:
| Type | Description |
|---|---|
Any
|
The matplotlib Axes used for plotting. |
Source code in src/vote_simulation/models/results/total_result.py
plot_metric_heatmap(row_param='n_voters', col_param='n_candidates', *, metric='mean_distance', ax=None, annotate=True, show=True, save_path=None)
¶
Heatmap of a scalar metric pivoted across two parameters.
The remaining (third) parameter must have a single distinct value
— use :meth:filter first if needed.
Source code in src/vote_simulation/models/results/total_result.py
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plot_metrics_rules_matrix(row_param='n_voters', col_param='n_candidates', *, stat='mean', metrics=None, annotate=True, fmt='.3f', cell_fontsize=None, show=True, save_path=None)
¶
Heatmap with rules as columns and metrics as rows.
Each cell shows the aggregated statistic (stat) for a given
(metric, rule) pair, averaged over all series currently in the
object (use :meth:filter to restrict the scope first).
The color scale is normalised per row (per metric) so that the gradient is uniform within each row and rules can be directly compared regardless of the absolute scale of each metric.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
row_param
|
str
|
Used only to derive a description of fixed parameters in the title. Filtering is the recommended way to narrow down the data. |
'n_voters'
|
col_param
|
str
|
Same as row_param. |
'n_candidates'
|
stat
|
str
|
|
'mean'
|
metrics
|
list[str] | None
|
Explicit list of metric fields (rows). When None all
fields in :data: |
None
|
annotate
|
bool
|
Whether to print raw values inside each cell. |
True
|
fmt
|
str
|
Format string used for annotations (e.g. |
'.3f'
|
cell_fontsize
|
int | None
|
Font size for cell annotations. When None
(default) the size is chosen automatically based on the number
of rules (smaller when there are many rules). Pass an
explicit integer (e.g. |
None
|
show
|
bool
|
Whether to call |
True
|
save_path
|
str | None
|
Optional file path to save the figure. |
None
|
Returns:
| Type | Description |
|---|---|
Any
|
The matplotlib Axes used for plotting. |
Source code in src/vote_simulation/models/results/total_result.py
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plot_rule_pair_heatmap(rule_a, rule_b, row_param='n_voters', col_param='n_candidates', *, ax=None, annotate=True, show=True, save_path=None)
¶
Heatmap of one rule-pair distance across two parameters.
Source code in src/vote_simulation/models/results/total_result.py
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plot_rules_2d(ax=None, *, show=True, save_path=None)
¶
Plot rules as labeled points in a 2D MDS projection.
Distances between points approximate the global mean pairwise rule
distances, averaged over all series in this result. Use
:meth:filter to restrict the scope first.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
ax
|
Any | None
|
Optional matplotlib Axes. A new figure is created when None. |
None
|
show
|
bool
|
Whether to call |
True
|
save_path
|
str | None
|
Optional file path to save the figure. |
None
|
Returns:
| Type | Description |
|---|---|
Any
|
The matplotlib Axes used for plotting. |
Source code in src/vote_simulation/models/results/total_result.py
plot_rules_3d(ax=None, *, show=True, save_path=None)
¶
Plot rules as labeled points in a 3D MDS projection.
Distances between points approximate the global mean pairwise rule
distances, averaged over all series in this result. Use
:meth:filter to restrict the scope first.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
ax
|
Any | None
|
Optional matplotlib 3D Axes. A new figure is created when None. |
None
|
show
|
bool
|
Whether to call |
True
|
save_path
|
str | None
|
Optional file path to save the figure. |
None
|
Returns:
| Type | Description |
|---|---|
Any
|
The matplotlib Axes used for plotting. |
Source code in src/vote_simulation/models/results/total_result.py
plot_winner_metric_heatmap(metric_field, rule_code, row_param='n_voters', col_param='n_candidates', *, stat='mean', ax=None, annotate=True, show=True, save_path=None)
¶
Heatmap of one winner metric for one rule, pivoted across two parameters.
Analogous to :meth:plot_metric_heatmap but for
:class:~vote_simulation.models.rules.WinnerMetrics fields instead of
rule-distance metrics.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
metric_field
|
str
|
One of the fields in
:data: |
required |
rule_code
|
str
|
Normalised rule code to inspect (e.g. |
required |
row_param
|
str
|
Row axis — |
'n_voters'
|
col_param
|
str
|
Column axis (same choices). |
'n_candidates'
|
stat
|
str
|
|
'mean'
|
ax
|
Any | None
|
Optional matplotlib Axes. A new figure is created when None. |
None
|
annotate
|
bool
|
Whether to print cell values on the heatmap. |
True
|
show
|
bool
|
Whether to call |
True
|
save_path
|
str | None
|
Optional file path to save the figure. |
None
|
Returns:
| Type | Description |
|---|---|
Any
|
The matplotlib Axes used for plotting. |
Source code in src/vote_simulation/models/results/total_result.py
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plot_winner_metrics_grid(rule_code, row_param='n_voters', col_param='n_candidates', *, stat='mean', metrics=None, annotate=True, show=True, save_path=None)
¶
Grid of heatmaps — one panel per winner metric — for a single rule.
Iterates over every field in
:data:~vote_simulation.models.rules.winner_metrics.METRIC_FIELDS (or
the subset given by metrics) and draws each as a heatmap panel,
using the same axes as :meth:plot_winner_metric_heatmap.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
rule_code
|
str
|
Normalised rule code to inspect (e.g. |
required |
row_param
|
str
|
Row axis — |
'n_voters'
|
col_param
|
str
|
Column axis (same choices). |
'n_candidates'
|
stat
|
str
|
|
'mean'
|
metrics
|
list[str] | None
|
Explicit list of metric fields to plot. When None all
fields in :data: |
None
|
annotate
|
bool
|
Whether to print cell values on each panel. |
True
|
show
|
bool
|
Whether to call |
True
|
save_path
|
str | None
|
Optional file path to save the whole figure. |
None
|
Returns:
| Type | Description |
|---|---|
Any
|
The 2-D NumPy array of matplotlib Axes. |
Source code in src/vote_simulation/models/results/total_result.py
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replace_series(series)
¶
rule_pair_frame(rule_a, rule_b)
¶
Mean distance between two rules in every series.
Returns a DataFrame with columns gen_model, n_voters,
n_candidates, distance.
Source code in src/vote_simulation/models/results/total_result.py
save_to_dir(dir_path)
¶
Persist every series as <label>.parquet inside dir_path.
Source code in src/vote_simulation/models/results/total_result.py
summary_frame()
¶
One-row-per-series DataFrame with key fields and scalar metrics.
Columns: gen_model, n_voters, n_candidates,
step_count, n_iterations, mean_distance,
most_distant_rule_a, most_distant_rule_b,
most_distant_distance.